Answer: refer to the following: The pH of a solution is a measure of the molar

evaluate exactly (without using a calculator). 24

evaluate exactly (without using a calculator). 34

evaluate exactly (without using a calculator). 52

evaluate exactly (without using a calculator). 43

evaluate exactly (without using a calculator). 82/3

evaluate exactly (without using a calculator). 272/3

evaluate exactly (without using a calculator).

evaluate exactly (without using a calculator).

evaluate exactly (without using a calculator). 50

evaluate exactly (without using a calculator). 60

approximate with a calculator. Round your answer to four decimal places. 41.2

approximate with a calculator. Round your answer to four decimal places. 41.2

approximate with a calculator. Round your answer to four decimal places.

approximate with a calculator. Round your answer to four decimal places.

approximate with a calculator. Round your answer to four decimal places. e2

approximate with a calculator. Round your answer to four decimal places. e1/2

approximate with a calculator. Round your answer to four decimal places. ep

approximate with a calculator. Round your answer to four decimal places. e-22

for the functions f(x)  3x, , and h(x)  10x1, nd the function value at the indicated points. f(3)

for the functions f(x)  3x, , and h(x)  10x1, nd the function value at the indicated points. h(1)

for the functions f(x)  3x, , and h(x)  10x1, nd the function value at the indicated points. g(1)

for the functions f(x)  3x, , and h(x)  10x1, nd the function value at the indicated points. f(2)

for the functions f(x)  3x, , and h(x)  10x1, nd the function value at the indicated points.

for the functions f(x)  3x, , and h(x)  10x1, nd the function value at the indicated points.

for the functions f(x)  3x, , and h(x)  10x1, nd the function value at the indicated points. f(e)

for the functions f(x)  3x, , and h(x)  10x1, nd the function value at the indicated points. g(p)

match the graph with the function.y  5x1

match the graph with the function. y  51

match the graph with the function.y  5x

match the graph with the function. y 5

match the graph with the function. y  1  5

match the graph with the function.y  5x  1

graph the exponential function using transformations. State the y-intercept, two additional points, the domain, the range, and the horizontal asymptote. f(x)  6x

graph the exponential function using transformations. State the y-intercept, two additional points, the domain, the range, and the horizontal asymptote. f(x)  7x

graph the exponential function using transformations. State the y-intercept, two additional points, the domain, the range, and the horizontal asymptote. (x)  10x

graph the exponential function using transformations. State the y-intercept, two additional points, the domain, the range, and the horizontal asymptote. f(x)  4x

graph the exponential function using transformations. State the y-intercept, two additional points, the domain, the range, and the horizontal asymptote. f(x)  ex

graph the exponential function using transformations. State the y-intercept, two additional points, the domain, the range, and the horizontal asymptote. f(x)  ex

graph the exponential function using transformations. State the y-intercept, two additional points, the domain, the range, and the horizontal asymptote. f(x)  2x  1

graph the exponential function using transformations. State the y-intercept, two additional points, the domain, the range, and the horizontal asymptote. f(x)  3x  1

graph the exponential function using transformations. State the y-intercept, two additional points, the domain, the range, and the horizontal asymptote. f(x)  2  ex

graph the exponential function using transformations. State the y-intercept, two additional points, the domain, the range, and the horizontal asymptote. f(x)  1  ex

graph the exponential function using transformations. State the y-intercept, two additional points, the domain, the range, and the horizontal asymptote. f(x)  ex1  4

graph the exponential function using transformations. State the y-intercept, two additional points, the domain, the range, and the horizontal asymptote. f(x)  ex1  2

graph the exponential function using transformations. State the y-intercept, two additional points, the domain, the range, and the horizontal asymptote. f(x)  3ex2

graph the exponential function using transformations. State the y-intercept, two additional points, the domain, the range, and the horizontal asymptote. f(x)  2ex

graph the exponential function using transformations. State the y-intercept, two additional points, the domain, the range, and the horizontal asymptote.

graph the exponential function using transformations. State the y-intercept, two additional points, the domain, the range, and the horizontal asymptote. f(x) = 2 - A1 3Bx+1f

Population Doubling Time. In 2002, there were 7.1 million people living in London, England. If the population is expected to double by 2090, what is the expected population in London in 2050?

Population Doubling Time. In 2004, the population in Morganton, Georgia, was 43,000. The population in Morganton is expected to double by 2010. If the growth rate remains the same, what is the expected population in Morganton in 2020?

Investments. Suppose an investor buys land in a rural area for $1500 an acre and sells some of it 5 years later at $3000 an acre and the rest of it 10 years later at $6000. Write a function that models the value of land in that area, assuming the growth rate stays the same. What would the expected cost per acre be 30 years after the initial investment of $1500?

Salaries. Twin brothers, Collin and Cameron, get jobs immediately after graduating from college at the age of 22. Collin opts for the higher starting salary, $55,000, and stays with the same company until he retires at 65. His salary doubles every 15 years. Cameron opts for a lower starting salary, $35,000, but moves to a new job every 5 years; he doubles his salary every 10 years until he retires at 65. What is the annual salary of each brother upon retirement?

Radioactive Decay. A radioactive isotope of selenium 75Se used in the creation of medical images of the pancreas, has a half-life of 119.77 days. If 200 milligrams are given to a patient, how many milligrams are left after 30 days?

Radioactive Decay. The radioactive isotope indium-111 (111In), used as a diagnostic tool for locating tumors associated with prostate cancer, has a half-life of 2.807 days. If 300 milligrams are given to a patient, how many milligrams will be left after a week?

Depreciation of Furniture. A couple buys a new bedroom set for $8000 and 10 years later sells it for $4000. If the depreciation continues at the same rate, how much would the bedroom set be worth in 4 more years?

Depreciation of a Computer. A student buys a new laptop for $1500 when she arrives as a freshman. A year later, the computer is worth approximately $750. If the depreciation continues at the same rate, how much would she expect to sell her laptop for when she graduates 4 years after she bought it?

Compound Interest. If you put $3200 in a savings account that earns 2.5% interest per year compounded quarterly, how much would you expect to have in that account in 3 years?

Compound Interest. If you put $10,000 in a savings account that earns 3.5% interest per year compounded annually, how much would you expect to have in that account in 5 years?

Compound Interest. How much money should you put in a savings account now that earns 5% a year compounded daily if you want to have $32,000 in 18 years?

Compound Interest. How much money should you put in a savings account now that earns 3.0% a year compounded weekly if you want to have $80,000 in 15 years?

Compound Interest. If you put $3200 in a savings account that pays 2% a year compounded continuously, how much will you have in the account in 15 years?

Compound Interest. If you put $7000 in a money market account that pays 4.3% a year compounded continuously, how much will you have in the account in 10 years?

Compound Interest. How much money should you deposit into a money market account that pays 5% a year compounded continuously to have $38,000 in the account in 20 years?

Compound Interest. How much money should you deposit into a certicate of deposit that pays 6% a year compounded continuously to have $80,000 in the account in 18 years?

refer to the following: Exponential functions can be used to model the concentration of a drug in a patients body. Suppose the concentration of Drug X in a patients bloodstream is modeled by where C(t) represents the concentration at time t (in hours), C0 is the concentration of the drug in the blood immediately after injection, and is a constant indicating the removal of the drug by the body through metabolism and/or excretion. The rate constant r has units of 1/time (1/hr). It is important to note that this model assumes that the blood concentration of the drug C0 peaks immediately when the drug is injected. Health/Medicine. After an injection of Drug Y, the concentration of the drug in the bloodstream drops at the rate of 0.020 1/hr. Find the concentration, to the nearest tenth, of the drug 20 hours after receiving an injection with initial concentration of 5.0 mg/L.

refer to the following: Exponential functions can be used to model the concentration of a drug in a patients body. Suppose the concentration of Drug X in a patients bloodstream is modeled by where C(t) represents the concentration at time t (in hours), C0 is the concentration of the drug in the blood immediately after injection, and is a constant indicating the removal of the drug by the body through metabolism and/or excretion. The rate constant r has units of 1/time (1/hr). It is important to note that this model assumes that the blood concentration of the drug C0 peaks immediately when the drug is injected. Health/Medicine. After an injection of Drug Y, the concentration of the drug in the bloodstream drops at the rate of 0.009 1/hr. Find the concentration, to the nearest tenth, of the drug 4 hours after receiving an injection with initial concentration of 4.0 mg/L.

refer to the following: The demand for a product, in thousands of units, can be expressed by the exponential demand function where p is the price per unit.

refer to the following: The demand for a product, in thousands of units, can be expressed by the exponential demand function where p is the price per unit.

explain the mistake that is made. Evaluate the expression 412. Solution: The correct value is . What mistake was made?

explain the mistake that is made. Evaluate the function for the given x: f(x)  4x for Solution: The correct value is 8. What mistake was made?

explain the mistake that is made. If $2000 is invested in a savings account that earns 2.5% interest compounding continuously, how much will be in the account in one year? Solution: Write the compound continuous interest formula. A  Pert Substitute P  2000, r  2.5, and t  1. A  2000e(2.5)(1) Simplify. A  24,364.99 This is incorrect. What mistake was made?

explain the mistake that is made. If $5000 is invested in a savings account that earns 3% interest compounding continuously, how much will be in the account in 6 months? Solution: Write the compound continuous interest formula. A  Pert Substitute P  5000, r  0.03, and t  6. A  5000e(0.03)(6) Simplify. A  5986.09 This is incorrect. What mistake was made?

determine whether each statement is true or false. The function f(x)  ex has the y-intercept (0,1).

determine whether each statement is true or false. The function f(x)  ex has a horizontal asymptote along the x-axis.

determine whether each statement is true or false. The functions y  3x and have the same graphs.

determine whether each statement is true or false. e  2.718.

Plot f(x)  3x and its inverse on the same graph.

Plot f(x)  ex and its inverse on the same graph.

Graph f(x)  ex.

Graph f(x)  ex.

Find the y-intercept and horizontal asymptote of f(x)  bex1  a.

Find the y-intercept and horizontal asymptote of f(x)  a  bex1.

Graph f(x)  b x, b  1, and state the domain.

Graph the function

Plot the function . What is the horizontal asymptote as x increases?

Plot the functions y 2x, y  ex, and y 3x in the same viewing screen. Explain why y  ex lies between the other two graphs.

Plot y1  ex and in the same viewing screen. What do you notice?

Plot y1  ex and in the same viewing screen. What do you notice?

Plot the functions and in the same viewing screen. Compare their horizontal asymptotes as x increases. What can you say about the function values of f, g, and h in terms of the powers of e as x increases?

Plot the functions and in the same viewing screen. Compare their horizontal asymptotes as x increases. What can you say about the function values of f, g, and h in terms of the powers of e as x increases?

Newtons Law of Heating and Cooling: Have you ever heated soup in a microwave and, upon taking it out, have it seem to cool considerably in the matter of minutes? Or has your ice-cold soda become tepid in just moments while outside on a hot summers day? This phenomenon is based on the so-called Newtons Law of Heating and Cooling. Eventually, the soup will cool so that its temperature is the same as the temperature of the room in which it is being kept, and the soda will warm until its temperature is the same as the outside temperature. Consider the following data: a. Form a scatterplot for this data. b. Use ExpReg to nd the best t exponential function for this data set, and superimpose its graph on the scatterplot. How good is the t? c. Use the best t exponential curve from (b) to answer the following: i. What will the predicted temperature of the soup be at 6 minutes? ii. What was the temperature of the soup the moment it was taken out of the microwave? d. Assume the temperature of the house is 72 F. According to Newtons Law of Heating and Cooling, the temperature of the soup should approach 72 . In light of this, comment on the shortcomings of the best t exponential curve.

Newtons Law of Heating and Cooling: Have you ever heated soup in a microwave and, upon taking it out, have it seem to cool considerably in the matter of minutes? Or has your ice-cold soda become tepid in just moments while outside on a hot summers day? This phenomenon is based on the so-called Newtons Law of Heating and Cooling. Eventually, the soup will cool so that its temperature is the same as the temperature of the room in which it is being kept, and the soda will warm until its temperature is the same as the outside temperature. Consider the following data: a. Form a scatterplot for this data. b. Use ExpReg to nd the best t exponential function for this data set, and superimpose its graph on the scatterplot. How good is the t? c. Use the best t exponential curve from (b) to answer the following: i. What will the predicted temperature of the soda be at 10 minutes? ii. What was the temperature of the soda the moment it was taken out of the refrigerator? d. Assume the temperature of the house is 90 F. According to Newtons Law of Heating and Cooling, the temperature of the soda should approach 90 . In light of this, comment on the shortcomings of the best t exponential curve.

write each logarithmic equation in its equivalent exponential form. log5 125  3

write each logarithmic equation in its equivalent exponential form. log3 27  3

write each logarithmic equation in its equivalent exponential form.

write each logarithmic equation in its equivalent exponential form.

write each logarithmic equation in its equivalent exponential form.

write each logarithmic equation in its equivalent exponential form.

write each logarithmic equation in its equivalent exponential form. log 0.01  2

write each logarithmic equation in its equivalent exponential form. log 0.0001  4

write each logarithmic equation in its equivalent exponential form. log 10,000  4

write each logarithmic equation in its equivalent exponential form. log 1000  3

write each logarithmic equation in its equivalent exponential form. log1>4 (64)  3

write each logarithmic equation in its equivalent exponential form. log1>6 (36)  2

write each logarithmic equation in its equivalent exponential form.

write each logarithmic equation in its equivalent exponential form. 1  ln e

write each logarithmic equation in its equivalent exponential form. ln 1  0

write each logarithmic equation in its equivalent exponential form. log 1  0

write each logarithmic equation in its equivalent exponential form. ln 5  x

write each logarithmic equation in its equivalent exponential form. ln 4  y

write each logarithmic equation in its equivalent exponential form. z  logx y

write each logarithmic equation in its equivalent exponential form. y  logx z

write each exponential equation in its equivalent logarithmic form. 83  512

write each exponential equation in its equivalent logarithmic form. 26  64

write each exponential equation in its equivalent logarithmic form. . 0.00001  105

write each exponential equation in its equivalent logarithmic form. 100,000  105

write each exponential equation in its equivalent logarithmic form. 15 = 1225

write each exponential equation in its equivalent logarithmic form.

write each exponential equation in its equivalent logarithmic form.

write each exponential equation in its equivalent logarithmic form.

write each exponential equation in its equivalent logarithmic form.

write each exponential equation in its equivalent logarithmic form.

write each exponential equation in its equivalent logarithmic form. ex  6

write each exponential equation in its equivalent logarithmic form. ex  4

write each exponential equation in its equivalent logarithmic form. x  yz

write each exponential equation in its equivalent logarithmic form. z  yx

evaluate the logarithms exactly (if possible). log2 1

evaluate the logarithms exactly (if possible). log5 1

evaluate the logarithms exactly (if possible). log5 3125

evaluate the logarithms exactly (if possible). log3 729

evaluate the logarithms exactly (if possible). log 107

evaluate the logarithms exactly (if possible). log 102

evaluate the logarithms exactly (if possible). log1/4 4096

evaluate the logarithms exactly (if possible). log1/7 2401

evaluate the logarithms exactly (if possible). log 0

evaluate the logarithms exactly (if possible). ln 0

evaluate the logarithms exactly (if possible). log(100)

evaluate the logarithms exactly (if possible). ln(1)

approximate (if possible) the common and natural logarithms using a calculator. Round to two decimal places. log 29

approximate (if possible) the common and natural logarithms using a calculator. Round to two decimal places. ln 29

approximate (if possible) the common and natural logarithms using a calculator. Round to two decimal places. ln 380

approximate (if possible) the common and natural logarithms using a calculator. Round to two decimal places. log 380

approximate (if possible) the common and natural logarithms using a calculator. Round to two decimal places. log 0

approximate (if possible) the common and natural logarithms using a calculator. Round to two decimal places. ln 0

approximate (if possible) the common and natural logarithms using a calculator. Round to two decimal places. ln 0.0003

approximate (if possible) the common and natural logarithms using a calculator. Round to two decimal places. log 0.0003

state the domain of the logarithmic function in interval notation. f(x)  log2(x  5)

state the domain of the logarithmic function in interval notation. f(x)  log2(4x  1)

state the domain of the logarithmic function in interval notation. f(x)  log3(5  2x)

state the domain of the logarithmic function in interval notation. f(x)  log3(5  x)

state the domain of the logarithmic function in interval notation. . f(x)  ln(7  2x)

state the domain of the logarithmic function in interval notation. f(x)  ln(3  x)

state the domain of the logarithmic function in interval notation.

state the domain of the logarithmic function in interval notation. f(x) = logx + 1

state the domain of the logarithmic function in interval notation. . f(x)  ln(7  2x)

state the domain of the logarithmic function in interval notation.

match the graph with the function. y  log5 x

match the graph with the function. y  log5(x)

match the graph with the function. y log5(x)

match the graph with the function. y  log5(x  3)  1

match the graph with the function. y  log5(1  x)  2

match the graph with the function. y log5(3  x)  2

graph the logarithmic function using transformation techniques. State the domain and range of f. f(x)  log(x  1)

graph the logarithmic function using transformation techniques. State the domain and range of f. f(x)  log(x  2)

graph the logarithmic function using transformation techniques. State the domain and range of f. ln x  2

graph the logarithmic function using transformation techniques. State the domain and range of f. ln x  1

graph the logarithmic function using transformation techniques. State the domain and range of f. f(x)  log3(x  2)  1

graph the logarithmic function using transformation techniques. State the domain and range of f. f(x)  log3(x  1)  2

graph the logarithmic function using transformation techniques. State the domain and range of f. f(x) log(x)  1

graph the logarithmic function using transformation techniques. State the domain and range of f. f(x)  log(x)  2

graph the logarithmic function using transformation techniques. State the domain and range of f. f(x)  ln(x  4)

graph the logarithmic function using transformation techniques. State the domain and range of f. f(x)  ln(4  x)

graph the logarithmic function using transformation techniques. State the domain and range of f. f(x)  log(2x)

graph the logarithmic function using transformation techniques. State the domain and range of f. f(x)  2ln(x)

refer to the following: Decibel: Sound. Calculate the decibels associated with normal conversation if the intensity is I  1 106 W/m2.

refer to the following: Decibel: Sound. Calculate the decibels associated with the onset of pain if the intensity is I  1 101 W/m2.

refer to the following: Decibel: Sound. Calculate the decibels associated with attending a football game in a loud college stadium if the intensity is I  1 100.3 W/m2.

refer to the following: Decibel: Sound. Calculate the decibels associated with a doorbell if the intensity is I  1 104.5 W/m2.

refer to the following: Richter Scale: Earthquakes. On Good Friday 1964, one of the most severe North American earthquakes ever recorded struck Alaska. The energy released measured 1.41 1017 joules. Calculate the magnitude of the 1964 Alaska earthquake using the Richter scale.

refer to the following: Richter Scale:Earthquakes. On January 22, 2003, Colima, Mexico, experienced a major earthquake. The energy released measured 6.31 1015 joules. Calculate the magnitude of the 2003 Mexican earthquake using the Richter scale

refer to the following: Richter Scale: Earthquakes. On December 26, 2003, a major earthquake rocked southeastern Iran. In Bam, 30,000 people were killed, and 85% of buildings were damaged or destroyed. The energy released measured 2 1014 joules. Calculate the magnitude of the 2003 Iran earthquake with the Richter scale.

refer to the following: Richter Scale:Earthquakes. On November 1, 1755, Lisbon was destroyed by an earthquake, which killed 90,000 people and destroyed 85% of the city. It was one of the most destructive earthquakes in history. The energy released measured 8 1017 joules. Calculate the magnitude of the 1755 Lisbon earthquake with the Richter scale.

refer to the following: The pH of a solution is a measure of the molar concentration of hydrogen ions, H in moles per liter, in the solution, which means that it is a measure of the acidity or basicity of the solution. The letters pH stand for power of hydrogen, and the numerical value is dened as Very acidic corresponds to pH values near 1, neutral corresponds to a pH near 7 (pure water), and very basic corresponds to values near 14. In the next six exercises you will be asked to calculate the pH value of wine, Pepto-Bismol, normal rainwater, bleach, and two fruits. List these six liquids and use your intuition to classify them as neutral, acidic, very acidic, basic, or very basic before you calculate their actual pH values. Chemistry. If wine has an approximate hydrogen ion concentration of 5.01 104, calculate its pH value.

refer to the following: The pH of a solution is a measure of the molar concentration of hydrogen ions, H in moles per liter, in the solution, which means that it is a measure of the acidity or basicity of the solution. The letters pH stand for power of hydrogen, and the numerical value is dened as Very acidic corresponds to pH values near 1, neutral corresponds to a pH near 7 (pure water), and very basic corresponds to values near 14. In the next six exercises you will be asked to calculate the pH value of wine, Pepto-Bismol, normal rainwater, bleach, and two fruits. List these six liquids and use your intuition to classify them as neutral, acidic, very acidic, basic, or very basic before you calculate their actual pH values. Chemistry. Pepto-Bismol has a hydrogen ion concentration of about 5.01 1011. Calculate its pH value.

refer to the following: The pH of a solution is a measure of the molar concentration of hydrogen ions, H in moles per liter, in the solution, which means that it is a measure of the acidity or basicity of the solution. The letters pH stand for power of hydrogen, and the numerical value is dened as Very acidic corresponds to pH values near 1, neutral corresponds to a pH near 7 (pure water), and very basic corresponds to values near 14. In the next six exercises you will be asked to calculate the pH value of wine, Pepto-Bismol, normal rainwater, bleach, and two fruits. List these six liquids and use your intuition to classify them as neutral, acidic, very acidic, basic, or very basic before you calculate their actual pH values. Chemistry. Normal rainwater is slightly acidic and has an approximate hydrogen ion concentration of 105.6. Calculate its pH value. Acid rain and tomato juice have similar approximate hydrogen ion concentrations of 104. Calculate the pH value of acid rain and tomato juice.

refer to the following: The pH of a solution is a measure of the molar concentration of hydrogen ions, H in moles per liter, in the solution, which means that it is a measure of the acidity or basicity of the solution. The letters pH stand for power of hydrogen, and the numerical value is dened as Very acidic corresponds to pH values near 1, neutral corresponds to a pH near 7 (pure water), and very basic corresponds to values near 14. In the next six exercises you will be asked to calculate the pH value of wine, Pepto-Bismol, normal rainwater, bleach, and two fruits. List these six liquids and use your intuition to classify them as neutral, acidic, very acidic, basic, or very basic before you calculate their actual pH values. Chemistry. Bleach has an approximate hydrogen ion concentration of 5.0 1013. Calculate its pH value.

refer to the following: The pH of a solution is a measure of the molar concentration of hydrogen ions, H in moles per liter, in the solution, which means that it is a measure of the acidity or basicity of the solution. The letters pH stand for power of hydrogen, and the numerical value is dened as Very acidic corresponds to pH values near 1, neutral corresponds to a pH near 7 (pure water), and very basic corresponds to values near 14. In the next six exercises you will be asked to calculate the pH value of wine, Pepto-Bismol, normal rainwater, bleach, and two fruits. List these six liquids and use your intuition to classify them as neutral, acidic, very acidic, basic, or very basic before you calculate their actual pH values. Chemistry. An apple has an approximate hydrogen ion concentration of 103.6. Calculate its pH value.

refer to the following: The pH of a solution is a measure of the molar concentration of hydrogen ions, H in moles per liter, in the solution, which means that it is a measure of the acidity or basicity of the solution. The letters pH stand for power of hydrogen, and the numerical value is dened as Very acidic corresponds to pH values near 1, neutral corresponds to a pH near 7 (pure water), and very basic corresponds to values near 14. In the next six exercises you will be asked to calculate the pH value of wine, Pepto-Bismol, normal rainwater, bleach, and two fruits. List these six liquids and use your intuition to classify them as neutral, acidic, very acidic, basic, or very basic before you calculate their actual pH values. Chemistry. An orange has an approximate hydrogen ion concentration of 104.2. Calculate its pH value.

Archaeology. Carbon dating is a method used to determine the age of a fossil or other organic remains. The age t in years is related to the mass C (in milligrams) of carbon 14 through a logarithmic equation: How old is a fossil that contains 100 milligrams of carbon 14?

Archaeology. Repeat Exercise 97, only now the fossil contains 40 milligrams of carbon 14.

Broadcasting. Decibels are used to quantify losses associated with atmospheric interference in a communication system. The ratio of the power (watts) received to the power transmitted (watts) is often compared. Often, watts are transmitted, but losses due to the atmosphere typically correspond to milliwatts being received: If 1 W of power is transmitted and 3 mW is received, calculate the power loss in dB.

Broadcasting. Repeat Exercise 99 assuming 3 W of power is transmitted and 0.2 mW is received.

refer to the following: The range of all possible frequencies of electromagnetic radiation is called the electromagnetic spectrum. In a vacuum the frequency of electromagnetic radiation is modeled by where c is m/s and is wavelength in meters. Physics/Electromagnetic Spectrum. The radio spectrum is the portion of the electromagnetic spectrum that corresponds to radio frequencies. The radio spectrum is used for various transmission technologies and is government regulated. Ranges of the radio spectrum are often allocated based on usage; for example, AM radio, cell phones, and television. (Source: http://en.wikipedia.org/wiki/Radio_spectrum) a. Complete the following table for the various usages of the radio spectrum. b. Graph the frequency within the radio spectrum (in Hertz) as a function of wavelength (in meters).

refer to the following: The range of all possible frequencies of electromagnetic radiation is called the electromagnetic spectrum. In a vacuum the frequency of electromagnetic radiation is modeled by where c is m/s and is wavelength in meters. Physics/Electromagnetic Spectrum. The visible spectrum is the portion of the electromagnetic spectrum that is visible to the human eye. Typically, the human eye can see wavelengths between 390 and 750 nm (nanometers or m). a. Complete the following table for the following colors of the visible spectrum. b. Graph the frequency (in Hertz) of the colors as a function of wavelength (in meters) on a log-log plot.

explain the mistake that is made. Evaluate the logarithm log2 4. Solution: Set the logarithm equal to x. log2 4  x Write the logarithm in exponential form. x  24 Simplify. x  16 Answer: log2 4  16 This is incorrect. The correct answer is log2 4  2. What went wrong?

explain the mistake that is made. Evaluate the logarithm log100 10. Solution: Set the logarithm equal to x. log100 10  x Express the equation in exponential form. 10x  100 Solve for x. x  2 Answer: log100 10  2 This is incorrect. The correct answer is What went wrong?

explain the mistake that is made. State the domain of the logarithmic function f(x)  log2(x  5) in interval notation. Solution: The domain of all logarithmic functions is x  0. Interval notation: (0, ) This is incorrect. What went wrong?

explain the mistake that is made. State the domain of the logarithmic function f(x)  ln in interval notation. Solution: Since the absolute value eliminates all negative numbers, the domain is the set of all real numbers. Interval notation: (, ) This is incorrect. What went wrong?

determine whether each statement is true or false. The domain of the standard logarithmic function, y  ln x, is the set of nonnegative real numbers.

determine whether each statement is true or false. The domain of the standard logarithmic function, y  ln x, is the set of nonnegative real numbers.

determine whether each statement is true or false. The horizontal axis is the horizontal asymptote of the graph of y  ln x. The graphs of y  log x and y  ln x have the same x-intercept (1, 0).

determine whether each statement is true or false. The graphs of y  log x and y  ln x have the same vertical asymptote, x  0.

State the domain, range, and x-intercept of the function f(x) ln(x  a)  b for a and b real positive numbers.

State the domain, range, and x-intercept of the function f(x)  log(a  x)  b for a and b real positive numbers.

Graph the function .

Graph the function . f(x) =b-ln(-x)

Use a graphing utility to graph y  ex and y  ln x in the same viewing screen. What line are these two graphs symmetric about?

Use a graphing utility to graph y  10x and y  log x in the same viewing screen. What line are these two graphs symmetric about?

Use a graphing utility to graph y  log x and y  ln x in the same viewing screen. What are the two common characteristics?

Using a graphing utility, graph . Is the function dened everywhere?

Use a graphing utility to graph f(x)  ln(3x), g(x)  ln 3  ln x, and h(x)  (ln 3)(ln x) in the same viewing screen. Determine the domain where two of the functions give the same graph.

Use a graphing utility to graph f(x)  ln(x2  4), g(x)  ln(x  2)  ln(x  2), and h(x)  ln(x  2)ln(x  2) in the same viewing screen. Determine the domain where two of the functions give the same graph.

refer to the following: Experimental data is collected all the time in biology and chemistry labs as scientists seek to understand natural phenomena. In biochemistry, the MichaelisMenten kinetics law describes the rates of enzyme reactions using the relationship between the rate of the reaction and the concentration of the substrate involved. The following data has been collected, where the velocity v is measured in mol/min of the enzyme reaction and the substrate level [S] is measured in mol/L. a. Create a scatterplot of this data by identifying [S] with the x-axis and v with the y-axis. b. The graph seems to be leveling off. Give an estimate of the maximum value the velocity might achieve. Call this estimate Vmax.c. Another constant of importance in describing the relationship between v and [S] is Km. This is the value of [S] that results in the velocity being half its maximum value. Estimate this value. Note: Km measures the afnity level of a particular enzyme to a particular substrate. The lower the value of Km, the higher the afnity. The higher the value of Km, the lower the afnity. d. The actual equation that governs the relationship between v and [S] is , which is NOT linear. This is the simple MichaelisMenten kinetics equation. i. Use LnReg to get a best t logarithmic curve for this data. Although the relationship between v and [S] is not logarithmic (rather, it is logistic), the best t logarithmic curve does not grow very quickly and so it serves as a reasonably good t. ii. At what [S] value, approximately, is the velocity 100 mol/min

refer to the following: Experimental data is collected all the time in biology and chemistry labs as scientists seek to understand natural phenomena. In biochemistry, the MichaelisMenten kinetics law describes the rates of enzyme reactions using the relationship between the rate of the reaction and the concentration of the substrate involved. The following data has been collected, where the velocity v is measured in mol/min of the enzyme reaction and the substrate level [S] is measured in mol/L. The MichaelisMenten equation can be arranged into various other forms that give a straight line (rather than a logistic curve) when one variable is plotted against another. One such rearrangement is the double-reciprocal LineweaverBurk equation. This equation plots the data values of the reciprocal of velocity (1/v) versus the reciprocal of the substrate level (1/[S]). The equation is as follows: Think of y as and x as a. What is the slope of the line? How about its y-intercept? b. Using the data from Exercise 121, we create two new columns for 1/v and 1/[S] to obtain the following data set: Create a scatterplot for the new data, treating x as 1/[S] and y as 1/v. c. Determine the best t line and value of r. d. Use the equation of the best t line in (c) to calculate Vmax. e. Use the above information to determine Km.

apply the properties of logarithms to simplify each expression. Do not use a calculator. log9 1

apply the properties of logarithms to simplify each expression. Do not use a calculator. log69 1

apply the properties of logarithms to simplify each expression. Do not use a calculator.

apply the properties of logarithms to simplify each expression. Do not use a calculator. log3.3 3.3

apply the properties of logarithms to simplify each expression. Do not use a calculator. log10 108

apply the properties of logarithms to simplify each expression. Do not use a calculator. ln e3

apply the properties of logarithms to simplify each expression. Do not use a calculator. log10 0.00

apply the properties of logarithms to simplify each expression. Do not use a calculator. log3 37

apply the properties of logarithms to simplify each expression. Do not use a calculator.

apply the properties of logarithms to simplify each expression. Do not use a calculator.

apply the properties of logarithms to simplify each expression. Do not use a calculator.

apply the properties of logarithms to simplify each expression. Do not use a calculator.

apply the properties of logarithms to simplify each expression. Do not use a calculator.

apply the properties of logarithms to simplify each expression. Do not use a calculator.

apply the properties of logarithms to simplify each expression. Do not use a calculator.

apply the properties of logarithms to simplify each expression. Do not use a calculator.

apply the properties of logarithms to simplify each expression. Do not use a calculator.

apply the properties of logarithms to simplify each expression. Do not use a calculator.

write each expression as a sum or difference of logarithms. logb(x3y5)

write each expression as a sum or difference of logarithms. logb(x3y5)

write each expression as a sum or difference of logarithms.logb(x1>2y1>3)

write each expression as a sum or difference of logarithms.logbA1r 1 3 tB

write each expression as a sum or difference of logarithms.

write each expression as a sum or difference of logarithms.

write each expression as a sum or difference of logarithms.

write each expression as a sum or difference of logarithms.

write each expression as a sum or difference of logarithms.

write each expression as a sum or difference of logarithms. log[(x  3)(x  2)]

write each expression as a sum or difference of logarithms.

write each expression as a sum or difference of logarithms.

write each expression as a sum or difference of logarithms.

write each expression as a sum or difference of logarithms.

write each expression as a single logarithm.Example: 2 log m + 5 log n = log(m2n5) 3 logbx  5 log

write each expression as a single logarithm.Example: 2 log m + 5 log n = log(m2n5) 2 logbu  3 logbv

write each expression as a single logarithm.Example: 2 log m + 5 log n = log(m2n5) 5 logbu  2 logbv

write each expression as a single logarithm.Example: 2 log m + 5 log n = log(m2n5) 3 logbx  logby

write each expression as a single logarithm.Example: 2 log m + 5 log n = log(m2n5)

write each expression as a single logarithm.Example: 2 log m + 5 log n = log(m2n5)

write each expression as a single logarithm.Example: 2 log m + 5 log n = log(m2n5) 2 logu  3 logv  2 logz

write each expression as a single logarithm.Example: 2 log m + 5 log n = log(m2n5) 3 logu  log2v  logz

write each expression as a single logarithm.Example: 2 log m + 5 log n = log(m2n5) ln(x  1)  ln(x  1)  2 ln(x2  3)

write each expression as a single logarithm.Example: 2 log m + 5 log n = log(m2n5) ln1x - 1 + ln1x + 1 - 2 ln(x2 - 1)

write each expression as a single logarithm.Example: 2 log m + 5 log n = log(m2n5)

write each expression as a single logarithm.Example: 2 log m + 5 log n = log(m2n5) 3 ln(x2 + 4) - 1 2 ln(x2 - 3) - ln(x - 1)

evaluate the logarithms using the change-of-base formula. Round to four decimal places. log5 7

evaluate the logarithms using the change-of-base formula. Round to four decimal places. log4 19

evaluate the logarithms using the change-of-base formula. Round to four decimal places. log12 5

evaluate the logarithms using the change-of-base formula. Round to four decimal places. log5 1 2

evaluate the logarithms using the change-of-base formula. Round to four decimal places. log2.7 5.2

evaluate the logarithms using the change-of-base formula. Round to four decimal places. log7.2 2.5

evaluate the logarithms using the change-of-base formula. Round to four decimal places. 10

evaluate the logarithms using the change-of-base formula. Round to four decimal places. 2.7

evaluate the logarithms using the change-of-base formula. Round to four decimal places.

evaluate the logarithms using the change-of-base formula. Round to four decimal places.

Sound. Sitting in the front row of a rock concert exposes us to a sound pressure (or sound level) of 1 101 W/m2 (or 110 dB), and a normal conversation is typically around 1 106 W/m2 (or 60 dB). How many decibels are you exposed to if a friend is talking in your ear at a rock concert? Note: 160 dB causes perforation of the eardrums. Hint: Add the sound pressures and convert to dB.

Sound. A whisper corresponds to 1 1010 W/m2 (or 20 dB), and a normal conversation is typically around 1 106 W/m2 (or 60 dB). How many decibels are you exposed to if one friend is whispering in your ear while the other one is talking at a normal level? Hint: Add the sound pressures and convert to dB.

There are two types of waves associated with an earthquake: compression and shear. The compression, or longitudinal, waves displace material behind the earthquakes path. Longitudinal waves travel at great speeds and are often called primary waves or simply P waves. Shear, or transverse, waves displace material at right angles to its path. Transverse waves do not travel as rapidly through the Earths crust and mantle as do longitudinal waves, and they are called secondary or S waves. Earthquakes. If a seismologist records the energy of P waves as 4.5 1012 joules and the energy of S waves as 7.8 108 joules, what is the total energy? What would the combined effect be on the Richter scale?

There are two types of waves associated with an earthquake: compression and shear. The compression, or longitudinal, waves displace material behind the earthquakes path. Longitudinal waves travel at great speeds and are often called primary waves or simply P waves. Shear, or transverse, waves displace material at right angles to its path. Transverse waves do not travel as rapidly through the Earths crust and mantle as do longitudinal waves, and they are called secondary or S waves. Earthquakes. Repeat Exercise 57 assuming the energy associated with the P waves is 5.2 1011 joules and the energy associated with the S waves is 4.1 109 joules.

simplify if possible and explain the mistake that is made. 3 log 5  log 25 Solution: Apply the quotient property (6). Write Apply the power property (7). Simplify. This is incorrect. The correct answer is log 5. What mistake was made?

simplify if possible and explain the mistake that is made. ln 3  2 ln 4  3 ln 2 Solution: Apply the power property (7). ln 3  ln 42  ln 23 Simplify. ln 3  ln 16  ln 8 Apply property (5). ln(3  16  8) Simplify. ln 11 This is incorrect. The correct answer is ln 64. What mistake was made?

simplify if possible and explain the mistake that is made. log2x  log3y  log4z Solution: Apply the product property (5). log6 xy  log4 z Apply the quotient property (6). log24xyz This is incorrect. What mistake was made?

simplify if possible and explain the mistake that is made. 2(log3  log5) Solution: Apply the quotient property (6). Apply the power property (7). Apply a calculator to approximate. This is incorrect. What mistake was made?

determine whether each statement is true or false.

determine whether each statement is true or false.

determine whether each statement is true or false.

determine whether each statement is true or false.

Prove the quotient rule: . Hint: Let and Write both in exponential form and nd the quotient

Prove the power rule: . Hint: Let . Write this log in exponential form, and nd logb Mp.

Write in terms of simpler logarithmic forms.

Show that logb a 1 x b =-logb x.

Use a graphing calculator to plot y  ln(2x) and y  ln 2  ln x. Are they the same graph?

Use a graphing calculator to plot y  ln(2  x) and y  ln 2  ln x. Are they the same graph?

Use a graphing calculator to plot and y  logx  log2. Are they the same graph?

Use a graphing calculator to plot and y = log y  logx  log2. Are they the same graph?

Use a graphing calculator to plot y  ln(x2) and y  2 ln x. Are they the same graph?

Use a graphing calculator to plot y  (ln x)2 and y  2 ln x. Are they the same graph?

Use a graphing calculator to plot y  ln x and . Are they the same graph?

Use a graphing calculator to plot y  log x and . Are they the same graph?

solve the exponential equations exactly for x.

solve the exponential equations exactly for x.

solve the exponential equations exactly for x.

solve the exponential equations exactly for x.

solve the exponential equations exactly for x.

solve the exponential equations exactly for x.

solve the exponential equations exactly for x.

solve the exponential equations exactly for x.

solve the exponential equations exactly for x.

solve the exponential equations exactly for x.

solve the exponential equations exactly for x.

solve the exponential equations exactly for x.

solve the exponential equations exactly for x.

solve the exponential equations exactly for x.

solve the exponential equations exactly for x.

solve the exponential equations exactly for x.

solve the exponential equations exactly for x.

solve the exponential equations exactly for x.

solve the exponential equations exactly and then approximate your answers to three decimal places.

solve the exponential equations exactly and then approximate your answers to three decimal places.

solve the exponential equations exactly and then approximate your answers to three decimal places.

solve the exponential equations exactly and then approximate your answers to three decimal places.

solve the exponential equations exactly and then approximate your answers to three decimal places.

solve the exponential equations exactly and then approximate your answers to three decimal places.

solve the exponential equations exactly and then approximate your answers to three decimal places.

solve the exponential equations exactly and then approximate your answers to three decimal places.

solve the exponential equations exactly and then approximate your answers to three decimal places.

solve the exponential equations exactly and then approximate your answers to three decimal places.

solve the exponential equations exactly and then approximate your answers to three decimal places.

solve the exponential equations exactly and then approximate your answers to three decimal places.

solve the exponential equations exactly and then approximate your answers to three decimal places.

solve the exponential equations exactly and then approximate your answers to three decimal places.

solve the exponential equations exactly and then approximate your answers to three decimal places.

solve the exponential equations exactly and then approximate your answers to three decimal places.

solve the exponential equations exactly and then approximate your answers to three decimal places.

solve the exponential equations exactly and then approximate your answers to three decimal places.

solve the exponential equations exactly and then approximate your answers to three decimal places.

solve the exponential equations exactly and then approximate your answers to three decimal places.

solve the exponential equations exactly and then approximate your answers to three decimal places.

solve the exponential equations exactly and then approximate your answers to three decimal places.

solve the exponential equations exactly and then approximate your answers to three decimal places.

solve the exponential equations exactly and then approximate your answers to three decimal places.

solve the exponential equations exactly and then approximate your answers to three decimal places.

solve the exponential equations exactly and then approximate your answers to three decimal places.

solve the logarithmic equations exactly.

solve the logarithmic equations exactly.

solve the logarithmic equations exactly.

solve the logarithmic equations exactly.

solve the logarithmic equations exactly.

solve the logarithmic equations exactly.

solve the logarithmic equations exactly.

solve the logarithmic equations exactly.

solve the logarithmic equations exactly.

solve the logarithmic equations exactly.

solve the logarithmic equations exactly.

solve the logarithmic equations exactly.

solve the logarithmic equations exactly.

solve the logarithmic equations exactly.

solve the logarithmic equations exactly.

solve the logarithmic equations exactly.

solve the logarithmic equations exactly.

solve the logarithmic equations exactly.

solve the logarithmic equations exactly,if possible; and then approximate your answers to three decimal places.

solve the logarithmic equations exactly,if possible; and then approximate your answers to three decimal places.

solve the logarithmic equations exactly,if possible; and then approximate your answers to three decimal places.

solve the logarithmic equations exactly,if possible; and then approximate your answers to three decimal places.

solve the logarithmic equations exactly,if possible; and then approximate your answers to three decimal places.

solve the logarithmic equations exactly,if possible; and then approximate your answers to three decimal places.

solve the logarithmic equations exactly,if possible; and then approximate your answers to three decimal places.

solve the logarithmic equations exactly,if possible; and then approximate your answers to three decimal places.

solve the logarithmic equations exactly,if possible; and then approximate your answers to three decimal places.

solve the logarithmic equations exactly,if possible; and then approximate your answers to three decimal places.

solve the logarithmic equations exactly,if possible; and then approximate your answers to three decimal places.

solve the logarithmic equations exactly,if possible; and then approximate your answers to three decimal places.

solve the logarithmic equations exactly,if possible; and then approximate your answers to three decimal places.

solve the logarithmic equations exactly,if possible; and then approximate your answers to three decimal places.

solve the logarithmic equations exactly,if possible; and then approximate your answers to three decimal places.

solve the logarithmic equations exactly,if possible; and then approximate your answers to three decimal places.

Health.After strenuous exercise Sandys heart rate R (beats per minute) can be modeled by where t is the number of minutes that have elapsed after she stops exercising. a. Find Sandys heart rate at the end of exercising (when she stops at time ). b. Determine how many minutes it takes after Sandy stops exercising for her heart rate to drop to 100 beats per minute. Round to the nearest minute. c. Find Sandys heart rate 15 minutes after she had stopped exercising.

Business.A local business purchased a new company van for $45,000. After 2 years the book value of the van is $30,000. a. Find an exponential model for the value of the van using where V is the value of the van in dollars and t is time in years. b. Approximately how many years will it take for the book value of the van to drop to $20,000?

Money. If money is invested in a savings account earning 3.5% interest compounded yearly, how many years will pass until the money triples?

Money. If money is invested in a savings account earning 3.5% interest compounded monthly, how many years will pass until the money triples?

Money. If $7500 is invested in a savings account earning 5% interest compounded quarterly, how many years will pass until there is $20,000?

Money. If $9000 is invested in a savings account earning 6% interest compounded continuously, how many years will pass until there is $15,000?

Earthquakes. On September 25, 2003 an earthquake that measured 7.4 on the Richter scale shook Hokkaido, Japan. How much energy (joules) did the earthquake emit?

Earthquakes.Again, on that same day (September 25, 2003), a second earthquake that measured 8.3 on the Richter scale shook Hokkaido, Japan. How much energy (joules) did the earthquake emit?

Sound. Matt likes to drive around campus in his classic Mustang with the stereo blaring. If his boom stereo has a sound intensity of 120 dB, how many watts per square meter does the stereo emit?

Sound. The New York Philharmonic has a sound intensity of 100 dB. How many watts per square meter does the orchestra emit?

Anesthesia. When a person has a cavity lled, the dentist typically administers a local anesthetic. After leaving the dentists ofce, ones mouth often remains numb for several more hours. If a shot of anesthesia is injected into the bloodstream at the time of the procedure (t  0), and the amount of anesthesia still in the bloodstream t hours after the initial injection is given by A  A0e0.5t, in how many hours will only 10% of the original anesthetic still be in the bloodstream?

Investments. Money invested in an account that compounds interest continuously at a rate of 3% a year is modeled by A  A0e0.03t, where A is the amount in the investment after t years and A0 is the initial investment. How long will it take the initial investment to double?

Biology. The U.S. Fish and Wildlife Service is releasing a population of the endangered Mexican gray wolf in a protected area along the New Mexico and Arizona border. They estimate the population of the Mexican gray wolf to be approximated by How many years will it take for the population to reach 100 wolves?

Introducing a New Car Model. If the number of new model Honda Accord hybrids purchased in North America is given by where t is the number of weeks after Honda releases the new model, how many weeks will it take after the release until there are 50,000 Honda hybrids from that batch on the road?

Earthquakes. A P wave measures 6.2 on the Richter scale, and an S wave measures 3.3 on the Richter scale. What is their combined measure on the Richter scale?

Sound. You and a friend get front row seats to a rock concert. The music level is 100 dB, and your normal conversation is 60 dB. If your friend is telling you something during the concert, how many decibels are you subjecting yourself to?

explain the mistake that is made. Solve the equation: 4ex  9. Solution: Take the natural log of both sides. ln(4ex)  ln 9 Apply the property of inverses. 4x  ln 9 Solve for x. This is incorrect. What mistake was made?

explain the mistake that is made. Solve the equation: log(x)  log(3)  1. Solution: Apply the product property (5). log(3x)  1 Exponentiate (base 10). 10log(3x)  1 Apply the properties of inverses. 3x  1 Solve for x. This is incorrect. What mistake was made?

explain the mistake that is made. Solve the equation: log(x)  log(x  3)  1 for x. Solution: Apply the product property (5). log(x2  3x)  1 Exponentiate both sides (base 10). Apply the property of inverses. x2  3x  10 Factor. (x  5)(x  2)  0 Solve for x. x 5 and x  2 This is incorrect. What mistake was made?

explain the mistake that is made. Solve the equation: log x  log 2  log 5. Solution: Combine the logarithms on the left. log(x  2)  log 5 Apply the property of one-to-one functions. x  2  5 Solve for x. x  3 This is incorrect. What mistake was made?

determine whether each statement is true or false. The sum of logarithms with the same base is equal to the logarithm of the product.

determine whether each statement is true or false. A logarithm squared is equal to two times the logarithm.

determine whether each statement is true or false. elog x  x

determine whether each statement is true or false. ex 2 has no solution.

Solve for x in terms of b:

Solve exactly: 2 logb(x)  2 logb(1  x)  4.

Solve for t in terms of y.

State the range of values of x such that the following identity holds: eln(x2-a) = x2 - a.

A function called the hyperbolic cosine is dened as the average of exponential growth and exponential decay by Find its inverse.

A function called the hyperbolic sine is dened by Find its inverse

Solve the equation ln 3x  ln(x2  1). Using a graphing calculator, plot the graphs y  ln(3x) and y  ln(x2  1) in the same viewing rectangle. Zoom in on the point where the graphs intersect. Does this agree with your solution?

Solve the equation Using a graphing calculator, plot the graphs and y  0.001x in the same viewing rectangle. Does this conrm your solution?

Use a graphing utility to help solve 3x  5x  2.

Use a graphing utility to help solve log x2  ln(x  3)  2.

Use a graphing utility to graph . State the domain. Determine if there are any symmetries and asymptotes.

Use a graphing utility to graph . State the domain. Determine if there are any symmetries and asymptotes.

match the function with the graph (a to f) and the model name (i to v).

match the function with the graph (a to f) and the model name (i to v).

match the function with the graph (a to f) and the model name (i to v).

match the function with the graph (a to f) and the model name (i to v).

match the function with the graph (a to f) and the model name (i to v).

match the function with the graph (a to f) and the model name (i to v).

Population Growth. The population of the Philippines in 2003 was 80 million. Their population increases 2.36% per year. What was the expected population of the Philippines in 2010? Apply the formula N  N0ert, where N represents the number of people.

Population Growth. Chinas urban population is growing at 2.5% a year, compounding continuously. If there were 13.7 million people in Shanghai in 1996, approximately how many people will there be in 2016? Apply the formula N  N0ert, where N represents the number of people.

Population Growth. Port St. Lucie, Florida, had the United States fastest growth rate among cities with a population of 100,000 or more between 2003 and 2004. In 2003, the population was 103,800 and increasing at a rate of 12% per year. In what year should the population reach 200,000? (Let t  0 correspond to 2003.) Apply the formula N  N0ert, where N represents the number of people.

Population Growth. San Franciscos population has been declining since the dot com bubble burst. In 2002, the population was 776,000. If the population is declining at a rate of 1.5% per year, in what year will the population be 700,000? (Let t  0 correspond to 2002.) Apply the formula N  N0ert, where N represents the number of people.

Cellular Phone Plans. The number of cell phones in China is exploding. In 2007, there were 487.4 million cell phone subscribers and the number was increasing at a rate of 16.5% per year. How many cell phone subscribers were there in 2010 according to this model? Use the formula N  N0ert, where N represents the number of cell phone subscribers. Let correspond to 2007.

Bacteria Growth. A colony of bacteria is growing exponentially. Initially 500 bacteria were in the colony. The growth rate is 20% per hour. (a) How many bacteria should be in the colony in 12 hours? (b) How many in one day? Use the formula N  N0ert, where N represents the number of bacteria.

Real Estate Appreciation. In 2004, the average house in Las Vegas cost $185,000, and real estate prices were increasing at an amazing rate of 30% per year. What was the expected cost of an average house in Las Vegas in 2007? Use the formula N  N0ert, where N represents the average cost of a home. Round to the nearest thousand.

Real Estate Appreciation. The average cost of a single-family home in California in 2004 was $230,000. In 2005, the average cost was $252,000. If this trend continued, what was the expected cost in 2007? Use the formula N  N0ert, where N represents the average cost of a home. Round to the nearest thousand.

Oceanography (Growth of Phytoplankton). Phytoplankton are microscopic plants that live in the ocean. Phytoplankton grow abundantly in oceans around the world and are the foundation of the marine food chain. One variety of phytoplankton growing in tropical waters is increasing at a rate of 20% per month. If it is estimated that there are 100 million in the water, how many will there be in 6 months? Utilize formula N  N0ert, where Nrepresents the population of phytoplankton.

Oceanography (Growth of Phytoplankton). In Arctic waters there are an estimated 50 million phytoplankton. The growth rate is 12% per month. How many phytoplankton will there be in 3 months? Utilize formula N  N0ert, where N represents the population of phytoplankton.

HIV/AIDS. In 2003, an estimated 1 million people had been infected with HIV in the United States. If the infection rate increases at an annual rate of 2.5% a year compounding continuously, how many Americans will be infected with the HIV virus by 2015?

HIV/AIDS. In 2003, there were an estimated 25 million people who have been infected with HIV in sub-Saharan Africa. If the infection rate increases at an annual rate of 9% a year compounding continuously, how many Africans will be infected with the HIV virus by 2015?

Anesthesia. When a person has a cavity lled, the dentist typically gives a local anesthetic. After leaving the dentists ofce, ones mouth often is numb for several more hours. If 100 ml of anesthesia is injected into the local tissue at the time of the procedure (t  0), and the amount of anesthesia still in the local tissue t hours after the initial injection is given by A  100e0.5t, how much is in the local tissue 4 hours later?

Anesthesia. When a person has a cavity lled, the dentist typically gives a local anesthetic. After leaving the dentists ofce, ones mouth often is numb for several more hours. If 100 ml of anesthesia is injected into the local tissue at the time of the procedure (t  0), and the amount of anesthesia still in the local tissue t hours after the initial injection is given by A  100e0.5t, how much is in the local tissue 12 hours later?

Business. The sales S (in thousands of units) of a new mp3 player after it has been on the market for t years can be modeled by a. If 350,000 units of the mp3 player were sold in the rst year, nd k to four decimal places. b. Use the model found in part (a) to estimate the sales of the mp3 player after it has been on the market for 3 years.

Business. During an economic downturn the annual prots of a company dropped from $850,000 in 2008 to $525,000 in 2010. Assume the exponential model for the annual prot where P is prot in thousands of dollars, and t is time in years. a. Find the exponential model for the annual prot. b. Assuming the exponential model is applicable in the year 2012, estimate the prot (to the nearest thousand dollars) for the year 2012.

Radioactive Decay. Carbon-14 has a half-life of 5730 years. How long will it take 5 grams of carbon-14 to be reduced to 2 grams?

Radioactive Decay. Radium-226 has a half-life of 1600 years. How long will it take 5 grams of radium-226 to be reduced to 2 grams?

Radioactive Decay. The half-life of uranium-238 is 4.5 billion years. If 98% of uranium-238 remains in a fossil, how old is the fossil?

Radioactive Decay. A drug has a half-life of 12 hours. If the initial dosage is 5 milligrams, how many milligrams will be in the patients body in 16 hours?

use the following formula for Newtons law of cooling. If you take a hot dinner out of the oven and place it on the kitchen countertop, the dinner cools until it reaches the temperature of the kitchen. Likewise, a glass of ice set on a table in a room eventually melts into a glass of water at that room temperature. The rate at which the hot dinner cools or the ice in the glass melts at any given time is proportional to the difference between its temperature and the temperature of its surroundings (in this case, the room). This is called Newtons law of cooling (or warming) and is modeled by where T is the temperature of an object at time t, Ts is the temperature of the surrounding medium, T0 is the temperature of the object at time t  0, t is the time, and k is a constant. Newtons Law of Cooling. An apple pie is taken out of the oven with an internal temperature of 325F. It is placed on a rack in a room with a temperature of 72F. After 10 minutes, the temperature of the pie is 200F. What will be the temperature of the pie 30 minutes after coming out of the oven?

use the following formula for Newtons law of cooling. If you take a hot dinner out of the oven and place it on the kitchen countertop, the dinner cools until it reaches the temperature of the kitchen. Likewise, a glass of ice set on a table in a room eventually melts into a glass of water at that room temperature. The rate at which the hot dinner cools or the ice in the glass melts at any given time is proportional to the difference between its temperature and the temperature of its surroundings (in this case, the room). This is called Newtons law of cooling (or warming) and is modeled by where T is the temperature of an object at time t, Ts is the temperature of the surrounding medium, T0 is the temperature of the object at time t  0, t is the time, and k is a constant. Newtons Law of Cooling. A cold drink is taken out of an ice chest with a temperature of 38F and placed on a picnic table with a surrounding temperature of 75F. After 5 minutes the temperature of the drink is 45F. What will the temperature of the drink be 20 minutes after it is taken out of the chest?

use the following formula for Newtons law of cooling. If you take a hot dinner out of the oven and place it on the kitchen countertop, the dinner cools until it reaches the temperature of the kitchen. Likewise, a glass of ice set on a table in a room eventually melts into a glass of water at that room temperature. The rate at which the hot dinner cools or the ice in the glass melts at any given time is proportional to the difference between its temperature and the temperature of its surroundings (in this case, the room). This is called Newtons law of cooling (or warming) and is modeled by where T is the temperature of an object at time t, Ts is the temperature of the surrounding medium, T0 is the temperature of the object at time t  0, t is the time, and k is a constant. Forensic Science (Time of Death). A body is discovered in a hotel room. At 7:00 A.M. a police detective found the bodys temperature to be 85F. At 8:30 A.M. a medical examiner measures the bodys temperature to be 82F. Assuming the room in which the body was found had a constant temperature of 74F, how long has the victim been dead? (Normal body temperature is 98.6F.)

use the following formula for Newtons law of cooling. If you take a hot dinner out of the oven and place it on the kitchen countertop, the dinner cools until it reaches the temperature of the kitchen. Likewise, a glass of ice set on a table in a room eventually melts into a glass of water at that room temperature. The rate at which the hot dinner cools or the ice in the glass melts at any given time is proportional to the difference between its temperature and the temperature of its surroundings (in this case, the room). This is called Newtons law of cooling (or warming) and is modeled by where T is the temperature of an object at time t, Ts is the temperature of the surrounding medium, T0 is the temperature of the object at time t  0, t is the time, and k is a constant. Forensic Science (Time of Death). At 4 A.M. a body is found in a park. The police measure the bodys temperature to be 90F. At 5 A.M. the medical examiner arrives and determines the temperature to be 86F. Assuming the temperature of the park was constant at 60F, how long has the victim been dead?

Depreciation of Automobile. A new Lexus IS250 has a book value of $38,000, and after one year it has a book value of $32,000. What is the cars value in 4 years? Apply the formula N  N0ert, where N represents the value of the car. Round to the nearest hundred.

Depreciation of Automobile. A new Hyundai Tiburon has a book value of $22,000, and after 2 years a book value of $14,000. What is the cars value in 4 years? Apply the formula N  N0ert, where N represents the value of the car. Round to the nearest hundred.

Automotive. A new model BMW convertible coupe is designed and produced in time to appear in North America in the fall. BMW Corporation has a limited number of new models available. The number of new model BMW convertible coupes purchased in North America is given by , where t is the number of weeks after the BMW is released. a. How many new-model BMW convertible coupes will have been purchased 2 weeks after the new model becomes available? b. How many after 30 weeks? c. What is the maximum number of new model BMW convertible coupes that will be sold in North America?

iPhone. The number of iPhones purchased is given by , where t is the time in weeks after they are made available for purchase. a. How many iPhones are purchased within the rst 2 weeks? b. How many iPhones are purchased within the rst month?

Cellular Phone Plans. The number of cell phones in China is exploding. In 2007, there were 487.4 million cell phone subscribers and the number was increasing at a rate of 16.5% per year. How many cell phone subscribers were there in 2010 according to this model? Use the formula N  N0ert, where N represents the number of cell phone subscribers. Let correspond to 2007.

Spread of a Virus. Dengue fever, an illness carried by mosquitoes, is occurring in one of the worst outbreaks in decades across Latin America and the Caribbean. In 2004, 300,000 cases were reported, and 630,000 cases in 2007. How many cases might be expected in 2013? (Let t  0 be 2004.) Use the formula N  N0ert, where N represents the number of cases.

Carrying Capacity. The Virginia Department of Fish and Game stocks a mountain lake with 500 trout. Ofcials believe the lake can support no more than 10,000 trout. The number of trout is given by , where t is time in years. How many years will it take for the trout population to reach 5000?

Carrying Capacity. The World Wildlife Fund has placed 1000 rare pygmy elephants in a conservation area in Borneo. They believe 1600 pygmy elephants can be supported in this environment. The number of elephants is given by , where t is time in years. How many years will it take the herd to reach 1200 elephants?

Lasers. The intensity of a laser beam is given by the ratio of power to area. A particular laser beam has an intensity function given by mW/cm2, where r is the radius off the center axis given in cm. Where is the beam brightest (largest intensity)?

Lasers. The intensity of a laser beam is given by the ratio of power to area. A particular laser beam has an intensity function given by mW/cm2, where r is the radius off the center axis given in cm. What percentage of the on-axis intensity (r  0) corresponds to r  2 cm?

Grade Distribution. Suppose the rst test in this class has a normal, or bell-shaped, grade distribution of test scores, with an average score of 75. An approximate function that models your classs grades on test 1 is , where N represents the number of students who received the score x. a. Graph this function. b. What is the average grade? c. Approximately how many students scored a 50? d. Approximately how many students scored 100?

Grade Distribution. Suppose the nal exam in this class has a normal, or bell-shaped, grade distribution of exam scores, with an average score of 80. An approximate function that models your classs grades on the exam is , where Nrepresents the number of students who received the score x. a. Graph this function. b. What is the average grade? c. Approximately how many students scored a 60? d. Approximately how many students scored 100?

Time to Pay Off Debt. Diana just graduated from medical school owing $80,000 in student loans. The annual interest rate is 9%. a. Approximately how many years will it take to pay off her student loan if she makes a monthly payment of $750? b. Approximately how many years will it take to pay off her loan if she makes a monthly payment of $1000?

Time to Pay Off Debt. Victor owes $20,000 on his credit card. The annual interest rate is 17%. a. Approximately how many years will it take him to pay off this credit card if he makes a monthly payment of $300? b. Approximately how many years will it take him to pay off this credit card if he makes a monthly payment of $400?

refer to the following: A local business borrows $200,000 to purchase property. The loan has an annual interest rate of 8% compounded monthly and a minimum monthly payment of $1467. Time to Pay Off Debt/Business. a. Approximately how many years will it take the business to pay off the loans if only the minimum payment is made? b. How much interest will the business pay over the life of the loan if only the minimum payment is made?

refer to the following: A local business borrows $200,000 to purchase property. The loan has an annual interest rate of 8% compounded monthly and a minimum monthly payment of $1467. Time to Pay Off Debt/Business. a. Approximately how many years will it take the business to pay off the loan if the minimum payment is doubled? b. How much interest will the business pay over the life of the loan if the minimum payment is doubled? c. How much in interest will the business save by doubling the minimum payment (see Exercise 45, part b)?

explain the mistake that is made. The city of Orlando, Florida, has a population that is growing at 7% a year, compounding continuously. If there were 1.1 million people in greater Orlando in 2006, approximately how many people will there be in 2016? Apply the formula N  N0ert, where N represents the number of people. Solution: Use the population growth model. N  N0ert Let N0  1.1, r  7, and t  10. N  1.1e(7)(10) Approximate with a calculator. 2.8 1030 This is incorrect. What mistake was made?

explain the mistake that is made. The city of San Antonio, Texas, has a population that is growing at 5% a year, compounding continuously. If there were 1.3 million people in the greater San Antonio area in 2006, approximately how many people will there be in 2016? Apply the formula N  N0ert, where Nrepresents the number of people. Solution: Use the population growth model. N  N0ert Let N0  1.3, r  5, and t  10. N  1.3e(5)(10) Approximate with a calculator. 6.7 1021 This is incorrect. What mistake was made?

determine whether each statement is true or false. When a species gets placed on an endangered species list, the species begins to grow rapidly, and then reaches a carrying capacity. This can be modeled by logistic growth.

determine whether each statement is true or false. A professor has 400 students one semester. The number of names (of her students) she can memorize can be modeled by a logarithmic function.

determine whether each statement is true or false. The spread of lice at an elementary school can be modeled by exponential growth.

determine whether each statement is true or false. If you purchase a laptop computer this year (t  0), then the value of the computer can be modeled with exponential decay.

refer to the logistic model where a is the carrying capacity. As c increases, does the model reach the carrying capacity in less time or more time?

refer to the logistic model where a is the carrying capacity. As k increases, does the model reach the carrying capacity in less time or more time?

Wing Shan just graduated from dental school owing $80,000 in student loans. The annual interest is 6%. Her time t to pay off the loan is given by where n is the number of payment periods per year and R is the periodic payment. a. Use a graphing utility to graph as Y1 and as Y2. Explain the difference in the two graphs. b. Use the key to estimate the number of years it will take Wing Shan to pay off her student loan if she can afford a monthly payment of $800. c. If she can make a biweekly payment of $400, estimate the number of years it will take her to pay off the loan. d. If she adds $200 more to her monthly or $100 more to her biweekly payment, estimate the number of years it will take her to pay off the loan.

Hong has a credit card debt in the amount of $12,000. The annual interest is 18%. His time t to pay off the loan is given by where n is the number of payment periods per year and R is the periodic payment. a. Use a graphing utility to graph as Y1 and as Y2. Explain the difference in the two graphs. b. Use the key to estimate the number of years it will take Hong to pay off his credit card if he can afford a monthly payment of $300. c. If he can make a biweekly payment of $150, estimate the number of years it will take him to pay off the credit card. d. If he adds $100 more to his monthly or $50 more to his biweekly payment, estimate the number of years it will take him to pay off the credit card.

Approximate each number using a calculator and round your answer to two decimal places. 84.7

Approximate each number using a calculator and round your answer to two decimal places.

Approximate each number using a calculator and round your answer to two decimal places.

Approximate each number using a calculator and round your answer to two decimal places. 1.21.2

Approximate each number using a calculator and round your answer to two decimal places. e3.2

Approximate each number using a calculator and round your answer to two decimal places. . e 

Approximate each number using a calculator and round your answer to two decimal places. 

Approximate each number using a calculator and round your answer to two decimal places. e-2.513e

Evaluate each exponential function for the given values. f(x)  24x f(2.2)

Evaluate each exponential function for the given values. . f(x)  2x4 f(1.3)

Evaluate each exponential function for the given values.

Evaluate each exponential function for the given values.

Match the graph with the function. y  2x2

Match the graph with the function. y 22x

Match the graph with the function. y  2  3x2

Match the graph with the function. y 2  32x

State the y-intercept and the horizontal asymptote and graph the exponential function. y 6x

State the y-intercept and the horizontal asymptote and graph the exponential function. y  4  3x

State the y-intercept and the horizontal asymptote and graph the exponential function. y  1  102x

State the y-intercept and the horizontal asymptote and graph the exponential function. y  4x  4

State the y-intercept and horizontal asymptote, and graph the exponential function.y  e2x

State the y-intercept and horizontal asymptote, and graph the exponential function.y  ex1

State the y-intercept and horizontal asymptote, and graph the exponential function.y  3.2ex3

State the y-intercept and horizontal asymptote, and graph the exponential function.y  2  e1x

Compound Interest. If $4500 is deposited into an account paying 4.5% compounding semiannually, how much will you have in the account in 7 years?

Compound Interest. How much money should be put in a savings account now that earns 4.0% a year compounded quarterly if you want $25,000 in 8 years?

Compound Interest. If $13,450 is put in a money market account that pays 3.6% a year compounded continuously, how much will be in the account in 15 years?

Compound Interest. How much money should be invested today in a money market account that pays 2.5% a year compounded continuously if you desire $15,000 in 10 years?

Write each logarithmic equation in its equivalent exponential form. log4 64  3

Write each logarithmic equation in its equivalent exponential form. log4 2 = 1 2

Write each logarithmic equation in its equivalent exponential form.

Write each logarithmic equation in its equivalent exponential form. log16 4 = 1

Write each exponential equation in its equivalent logarithmic form. 63  216

Write each exponential equation in its equivalent logarithmic form. 104  0.0001

Write each exponential equation in its equivalent logarithmic form.

Write each exponential equation in its equivalent logarithmic form.

Evaluate the logarithms exactly. log7 1

Evaluate the logarithms exactly. log4 256

Evaluate the logarithms exactly. log1/6 1296

Evaluate the logarithms exactly. log 1012

Approximate the common and natural logarithms utilizing a calculator. Round to two decimal places. log 32

Approximate the common and natural logarithms utilizing a calculator. Round to two decimal places. ln 32

Approximate the common and natural logarithms utilizing a calculator. Round to two decimal places. ln 0.125

Approximate the common and natural logarithms utilizing a calculator. Round to two decimal places. log 0.125

State the domain of the logarithmic function in interval notation. . f(x)  log3(x  2)

State the domain of the logarithmic function in interval notation. f(x)  log2(2  x)

State the domain of the logarithmic function in interval notation. f(x)  log(x2  3)

State the domain of the logarithmic function in interval notation. f(x)  log(3 x2)

Match the graph with the function. y  log7 x

Match the graph with the function. y log7 (x)

Match the graph with the function. y  log7 (x  1)  3

Match the graph with the function. y log7 (1  x)  3

Graph the logarithmic function with transformation techniques. f(x)  log4 (x  4)  2

Graph the logarithmic function with transformation techniques. f(x)  log4 (x  4)  3

Graph the logarithmic function with transformation techniques. f(x) log4 (x)  6

Graph the logarithmic function with transformation techniques. f(x) 2 log4 (x)  4

Chemistry. Calculate the pH value of milk, assuming it has a concentration of hydrogen ions given by H 3.16 107.

Chemistry. Calculate the pH value of Coca-Cola, assuming it has a concentration of hydrogen ions given by H2.0 103.

Sound. Calculate the decibels associated with a teacher speaking to a medium-sized class if the sound intensity is 1 107 W/m2.

Sound. Calculate the decibels associated with an alarm clock if the sound intensity is 1 104 W/m2.

Use the properties of logarithms to simplify each expression. log2.5 2.5

Use the properties of logarithms to simplify each expression.

Use the properties of logarithms to simplify each expression.

Use the properties of logarithms to simplify each expression. e3 ln 6

Write each expression as a sum or difference of logarithms. logc xayb

Write each expression as a sum or difference of logarithms. log3 x2y3

Write each expression as a sum or difference of logarithms.

Write each expression as a sum or difference of logarithms.

Write each expression as a sum or difference of logarithms.

Write each expression as a sum or difference of logarithms.

Evaluate the logarithms using the change-of-base formula. log8 3

Evaluate the logarithms using the change-of-base formula.

Evaluate the logarithms using the change-of-base formula.

Evaluate the logarithms using the change-of-base formula. log13 2.5

Solve the exponential equations exactly for x. e3x4  1

Solve the exponential equations exactly for x.

Solve the exponential equations exactly for x. e3x4  1

Solve the exponential equations exactly for x. e2x = e4.8

Solve the exponential equations exactly for x.

Solve the exponential equations exactly for x. 100x2-3 = 10A

Solve the exponential equation. Round your answer to three decimal places. e2x3  3  10

Solve the exponential equation. Round your answer to three decimal places. 22x1  3  17

Solve the exponential equation. Round your answer to three decimal places. e2x  6ex  5  0

Solve the exponential equation. Round your answer to three decimal places. 4e0.1x  64

Solve the exponential equation. Round your answer to three decimal places. (2x  2x)( 2x  2x)  0

Solve the exponential equation. Round your answer to three decimal places. 5(2x)  25

Solve the logarithmic equations exactly. log(3x)  2

Solve the logarithmic equations exactly. log3(x  2)  4

Solve the logarithmic equations exactly. log4 x  log4 2x  8

Solve the logarithmic equations exactly. log6 x  log6(2x  1)  log6 3

Solve the logarithmic equations. Round your answers to three decimal places. ln x2  2.2

Solve the logarithmic equations. Round your answers to three decimal places. ln(3x  4)  7

Solve the logarithmic equations. Round your answers to three decimal places. log3(2  x)  log3(x  3)  log3 x

Solve the logarithmic equations. Round your answers to three decimal places. 4 log(x  1)  2 log(x  1)  1

Compound Interest. If Tania needs $30,000 a year from now for a down payment on a new house, how much should she put in a 1-year CD earning 5% a year compounding continuously so that she will have exactly $30,000 a year from now?

Stock Prices. Jeremy is tracking the stock value of Best Buy (BBY on the NYSE). In 2003, he purchased 100 shares at $28 a share. The stock did not pay dividends because the company reinvested all earnings. In 2005, Jeremy cashed out and sold the stock for $4000. What was the annual rate of return on BBY?

Compound Interest. Money is invested in a savings account earning 4.2% interest compounded quarterly. How many years will pass until the money doubles?

Compound Interest. If $9000 is invested in an investment earning 8% interest compounded continuously, how many years will pass until there is $22,500?

Population. Nevada has the fastest growing population according to the U.S. Census Bureau. In 2004, the population of Nevada was 2.62 million and increasing at an annual rate of 3.5%. What is the expected population in 2014? (Let t 0 be 2004.) Apply the formula N  N0ert, where Nis the population.

Population. The Hispanic population in the United States is the fastest growing of any ethnic group. In 1996, there were an estimated 28.3 million Hispanics in the United States, and in 2000 there were an estimated 32.5 million. What is the expected population of Hispanics in the United States in 2014? (Let t  0 be 1996.) Apply the formula N  N0ert, where N is the population.

Bacteria Growth. Bacteria are growing exponentially. Initially, there were 1000 bacteria; after 3 hours there were 2500. How many bacteria should be expected in 6 hours? Apply the formula N  N0ert, where Nis the number of bacteria.

Population. In 2003, the population of Phoenix, Arizona, was 1,388,215. In 2004, the population was 1,418,041. What is the expected population in 2014? (Let t  0 be 2003.) Apply the formula N  N0ert, where N is the population.

Radioactive Decay. Strontium-90 has a half-life of 28 years. How long will it take for 20 grams of this to decay to 5 grams? Apply the formula N  N0ert, where N is the number of grams.

Radioactive Decay. Plutonium-239 has a half-life of 25,000 years. How long will it take for 100 grams to decay to 20 grams? Apply the formula N  N0ert, where N is the number of grams.

Wild Life Population. The Boston Globe reports that the sh population of the Essex River in Massachusetts is declining. In 2003, it was estimated there were 5600 sh in the river, and in 2004, there were only 2420 sh. How many should there have been in 2010 assuming the same trend? Apply the formula N  N0ert, where N is the number of sh.

Car Depreciation. A new Acura TSX costs $28,200. In 2 years the value will be $24,500. What is the expected value in 6 years? Apply the formula N  N0ert, where N is the value of the car.

Carrying Capacity. The carrying capacity of a species of beach mice in St. Croix is given by M  1000(1  e0.035t) where M is the number of mice and t is time in years (t  0 corresponds to 1998). How many mice were there in 2010 according to this model?

Population. The city of Brandon, Florida, had 50,000 residents in 1970, and since the crosstown expressway was built, its population has increased 2.3% per year. If the growth continues at the same rate, how many residents will Brandon have in 2030?

Use a graphing utility to graph the function f(x)  . Determine the horizontal asymptote as x increases.

Use a graphing utility to graph the functions y  ex2 and y  3x  1 in the same viewing screen. Estimate the coordinates of the point of intersection. Round your answers to three decimal places.

Use a graphing utility to graph the functions y  log2.4(3x  1) and y  log0.8(x  1)  3.5 in the same viewing screen. Estimate the coordinates of the point of intersection. Round your answers to three decimal places.

Use a graphing utility to graph the functions y  log2.5(x  1)  2 and y  3.5x2 in the same viewing screen. Estimate the coordinates of the point(s) of intersection. Round your answers to three decimal places.

Use a graphing utility to graph f(x)  log2 and g(x)  3 log2 x  log2(x  1)  log2(x  1) in the same viewing screen. Determine the domain where the two functions give the same graph.

Use a graphing utility to graph f(x)  ln and g(x)  ln (3  x)  ln (3  x)  ln(x  1)  ln(x  1) in the same viewing screen. Determine the domain where the two functions give the same graph.

Use a graphing utility to graph . State the domain.Determineifthereareanysymmetriesandasymptotes.

A drug with initial dosage of 4 milligrams has a half-life of 18 hours. Let (0, 4) and (18, 2) be two points. a. Determine the equation of the dosage. b. Use to model the equation of the dosage. c. Are the equations in (a) and (b) the same?

In Exercise 105, let t  0 be 2003 and (0, 5600) and (1, 2420) be the two points. a. Use to model the equation for the sh population. b. Using the equation found in (a), how many sh should have been expected in 2010? c. Does the answer in (b) agree with the answer in Exercise 105?

Simplify .

Use a calculator to evaluate log5 326 (round to two decimal places).

Find the exact value of log1/3 81.

Rewrite the expression in a form with no logarithms of products, quotients, or powers.

solve for x, exactly if possible. If an approximation is required, round your answer to three decimal places. ex2-1 = 42

solve for x, exactly if possible. If an approximation is required, round your answer to three decimal places. e2x  5ex  6  0

solve for x, exactly if possible. If an approximation is required, round your answer to three decimal places. 27e0.2x1  300

solve for x, exactly if possible. If an approximation is required, round your answer to three decimal places. 32x1  15

solve for x, exactly if possible. If an approximation is required, round your answer to three decimal places. 3 ln(x  4)  6

solve for x, exactly if possible. If an approximation is required, round your answer to three decimal places. log(6x  5)  log 3  log 2  log x

solve for x, exactly if possible. If an approximation is required, round your answer to three decimal places. ln(ln x)  1

solve for x, exactly if possible. If an approximation is required, round your answer to three decimal places. log2(3x  1)  log2(x  1)  log2(x  1)

solve for x, exactly if possible. If an approximation is required, round your answer to three decimal places. log6 x  log6(x  5)  2

solve for x, exactly if possible. If an approximation is required, round your answer to three decimal places. ln(x  2)  ln(x  3)  2

solve for x, exactly if possible. If an approximation is required, round your answer to three decimal places. ln x  ln(x  3)  1

solve for x, exactly if possible. If an approximation is required, round your answer to three decimal places. log2  3

solve for x, exactly if possible. If an approximation is required, round your answer to three decimal places.

solve for x, exactly if possible. If an approximation is required, round your answer to three decimal places. ln x  ln(x  3)  2

solve for x, exactly if possible. If an approximation is required, round your answer to three decimal places. State the domain of the function

solve for x, exactly if possible. If an approximation is required, round your answer to three decimal places. State the range of x values for which the following is true: 10log (4xa)  4x  a.

nd all intercepts and asymptotes, and graph. f(x)  3x  1

nd all intercepts and asymptotes, and graph. f(x) = A1 2Bx - 3

nd all intercepts and asymptotes, and graph. f(x)  ln(2x  3)  1

nd all intercepts and asymptotes, and graph. f(x)  log(1  x)  2

Interest. If $5000 is invested at a rate of 6% a year, compounded quarterly, what is the amount in the account after 8 years?

Interest. If $10,000 is invested at a rate of 5%, compounded continuously, what is the amount in the account after 10 years?

Sound. A lawn mowers sound intensity is approximately 1 103 W/m2. Assuming your threshold of hearing is 1 1012 W/m2, calculate the decibels associated with the lawn mower.

Population. The population in Seattle, Washington, has been increasing at a rate of 5% a year. If the population continues to grow at that rate, and in 2004 there are 800,000 residents, how many residents will there be in 2014? Hint: N  N0ert.

Earthquake. An earthquake is considered moderate if it is between 5 and 6 on the Richter scale. What is the energy range in joules for a moderate earthquake?

Radioactive Decay. The mass m(t) remaining after t hours from a 50-gram sample of a radioactive substance is given by the equation m(t)  50e0.0578t. After how long will only 30 grams of the substance remain? Round your answer to the nearest hour.

Bacteria Growth. The number of bacteria in a culture is increasing exponentially. Initially, there were 200 in the culture. After 2 hours there are 500. How many should beexpected in 8 hours? Round your answer to the nearest hundred.

Carbon Decay. Carbon-14 has a half-life of 5730 years. How long will it take for 100 grams to decay to 40 grams?

Spread of a Virus. The number of people infected by a virus is given by , where t is time in days. In how many days will 1000 people be infected?

Oil Consumption. The world consumption of oil was 76 million barrels per day in 2002. In 2004, the consumption was 83 million barrels per day. How many barrels should be expected to be consumed in 2014?

Use a graphing utility to graph . State the domain. Determine if there are any symmetries and asymptotes.

Use a graphing utility to help solve the equation 43x  2x  1. Round your answer to two decimal places.

Simplify and express in terms of positive exponents.

Simplify .

Solve using the quadratic formula: 5x2  4x  3.

Solve and check:

Solve and express the solution in interval notation:

Solve for x:

Write an equation of the line that is perpendicular to the line 4x  3y  6 and that passes through the point (7, 6).

Using the function f(x)  4x  x2, evaluate the difference quotient

Given the piecewise-dened function nd a. f(4) b. f(0) c. f(1) d. f(4) e. State the domain and range in interval notation. f. Determine the intervals where the function is increasing, decreasing, or constant.

Sketch the graph of the function and identify all transformations.

Determine whether the function is one-to-one.

Write an equation that describes the variation: R is inversely proportional to the square of d and R  3.8 when d  0.02.

Find the vertex of the parabola associated with the quadratic function f(x) 

Find a polynomial of minimum degree (there are many) that has the zeros x 5 (multiplicity 2) and x  9 (multiplicity 4).

Use synthetic division to nd the quotient Q(x) and remainder r(x) of (3x2  4x3  x4  7x  20)  (x  4).

Given the zero x  2  i of the polynomial P(x)  x4 7x3  13x2  x  20, determine all the other zeros and write the polynomial as the product of linear factors.

Find the vertical and slant asymptotes of

Graph the rational function . Give all asymptotes.

Without employing a calculator, give the exact value of

If $5400 is invested at 2.75% compounded monthly, how much is in the account after 4 years?

Give the exact value of log3 243.

Write the expression ln(x  5)  2 ln(x  1)  ln(3x) as a single logarithm.

Solve the logarithmic equation exactly: 102 log(4x9)  121.

Give an exact solution to the exponential equation .

If $8500 is invested at 4% compounded continuously, how many years will pass until there is $12,000?

Use a graphing utility to help solve the equation e32x2x1. Round your answer to two decimal places.

Strontium-90 with an initial amount of 6 grams has a half-life of 28 years. a. Use to model the equation of the amount remaining. b. How many grams will remain after 32 years? Round your answer to two decimal places.