Precalculus: Graphical, Numerical, Algebraic 8th Edition solutions

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1-4, prove that each function in the given pair is the inverse of the other. \(f(x)=e^{2 x}\) and \(g(x)=\ln \left(x^{1 / 2}\right)\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1-4, prove that each function in the given pair is the inverse of the other. \(f(x)=10^{x / 2}\) and \(g(x)=\log x^2, x>0\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1-4, prove that each function in the given pair is the inverse of the other. \(f(x)=(1 / 3) \ln x\) and \(g(x)=e^{3 x}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1-4, prove that each function in the given pair is the inverse of the other. \(f(x)=3 \log x^2, x>0\) and \(g(x)=10^{x / 6}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 5 and 6, write the number in scientific notation. The mean distance from Jupiter to the Sun is about 778,300,000 km.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 5 and 6, write the number in scientific notation. An atomic nucleus has a diameter of about 0.000000000000001 m.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 7 and 8, write the number in decimal form. Avogadros number is about \(6.02 \times 10^{23}\) .

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 7 and 8, write the number in decimal form. The atomic mass unit is about \(1.66 \times 10^{-27} \ \mathrm {kg}\) .

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 9 and 10, use scientific notation to simplify the expression; leave your answer in scientific notation. (186,000) (31,000,000)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 9 and 10, use scientific notation to simplify the expression; leave your answer in scientific notation. \(\frac {0.0000008}{0.000005}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1-10, find the exact solution algebraically, and check it by substituting into the original equation. \(36\left(\frac{1}{3}\right)^{x / 5}=4\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1-10, find the exact solution algebraically, and check it by substituting into the original equation. \(32\left(\frac{1}{4}\right)^{x / 3}=2\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1-10, find the exact solution algebraically, and check it by substituting into the original equation. \(2 \cdot 5^{x / 4}=250\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1-10, find the exact solution algebraically, and check it by substituting into the original equation. \(3 \cdot 4^{x / 2}=96\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1-10, find the exact solution algebraically, and check it by substituting into the original equation. \(2\left(10^{-x / 3}\right)=20\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1-10, find the exact solution algebraically, and check it by substituting into the original equation. \(3\left(5^{-x / 4}\right)=15\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1-10, find the exact solution algebraically, and check it by substituting into the original equation. log x=4

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1-10, find the exact solution algebraically, and check it by substituting into the original equation. \(\log _2 x=5\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1-10, find the exact solution algebraically, and check it by substituting into the original equation. \(\log _4(x-5)=-1\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1-10, find the exact solution algebraically, and check it by substituting into the original equation. \(\log _4(1-x)=1\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 11-18, solve each equation algebraically. Obtain a numerical approximation for your solution and check it by substituting into the original equation. \(1.06^x=4.1\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 11-18, solve each equation algebraically. Obtain a numerical approximation for your solution and check it by substituting into the original equation. \(0.98^x=1.6\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 11-18, solve each equation algebraically. Obtain a numerical approximation for your solution and check it by substituting into the original equation. \(50 e^{0.035 x}=200\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 11-18, solve each equation algebraically. Obtain a numerical approximation for your solution and check it by substituting into the original equation. \(80 e^{0.045 x}=240\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 11-18, solve each equation algebraically. Obtain a numerical approximation for your solution and check it by substituting into the original equation. \(3+2 e^{-x}=6\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 11-18, solve each equation algebraically. Obtain a numerical approximation for your solution and check it by substituting into the original equation. \(7-3 e^{-x}=2\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 11-18, solve each equation algebraically. Obtain a numerical approximation for your solution and check it by substituting into the original equation. 3 ln (x - 3) + 4 = 5

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 11-18, solve each equation algebraically. Obtain a numerical approximation for your solution and check it by substituting into the original equation. 3 - log (x + 2) = 5

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 19-24, state the domain of each function. Then match the function with its graph. (Each graph shown has a window of [-4.7,4.7] by [-3.1,3.1]). f(x) = log [x(x + 1)]

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 19-24, state the domain of each function. Then match the function with its graph. (Each graph shown has a window of [-4.7,4.7] by [-3.1,3.1]). g(x) = log x + log (x + 1)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 19-24, state the domain of each function. Then match the function with its graph. (Each graph shown has a window of [-4.7,4.7] by [-3.1,3.1]). \(f(x)=\ln \frac{x}{x+1}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 19-24, state the domain of each function. Then match the function with its graph. (Each graph shown has a window of [-4.7,4.7] by [-3.1,3.1]). g(x) = ln x - ln (x + 1)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 19-24, state the domain of each function. Then match the function with its graph. (Each graph shown has a window of [-4.7,4.7] by [-3.1,3.1]). f(x) = 2 ln x

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 19-24, state the domain of each function. Then match the function with its graph. (Each graph shown has a window of [-4.7,4.7] by [-3.1,3.1]). \(g(x)=\ln x^2\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2538, solve each equation by the method of your choice. Support your solution by a second method. \(\log x^2=6\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2538, solve each equation by the method of your choice. Support your solution by a second method. \( \ln x^2=4\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2538, solve each equation by the method of your choice. Support your solution by a second method. \(\log x^4=2\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2538, solve each equation by the method of your choice. Support your solution by a second method. \(\ln x^6=12\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2538, solve each equation by the method of your choice. Support your solution by a second method. \(\frac{2^x-2^{-x}}{3}=4\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2538, solve each equation by the method of your choice. Support your solution by a second method. \(\frac{2^x+2^{-x}}{2}=3\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2538, solve each equation by the method of your choice. Support your solution by a second method. \(\frac{e^x+e^{-x}}{2}=4\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2538, solve each equation by the method of your choice. Support your solution by a second method. \(2 e^{2 x}+5 e^x-3=0\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2538, solve each equation by the method of your choice. Support your solution by a second method. \(\frac{500}{1+25 e^{0.3 x}}=200\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2538, solve each equation by the method of your choice. Support your solution by a second method. \(\frac{400}{1+95 e^{-0.6 x}}=150\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2538, solve each equation by the method of your choice. Support your solution by a second method. \(\frac{1}{2} \ln (x+3)-\ln x=0\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2538, solve each equation by the method of your choice. Support your solution by a second method. \(\log x-\frac{1}{2} \log (x+4)=1\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2538, solve each equation by the method of your choice. Support your solution by a second method. ln (x - 3)+ ln (x + 4)=3 ln 2

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2538, solve each equation by the method of your choice. Support your solution by a second method. log (x-2) + log (x + 5) = 2 log 3

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 39-44, determine by how many orders of magnitude the quantities differ. A $100 bill and a dime

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 39-44, determine by how many orders of magnitude the quantities differ. A canary weighing 20 g and a hen weighing 2 kg

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 39-44, determine by how many orders of magnitude the quantities differ. An earthquake rated 7 on the Richter scale and one rated 5.5

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 39-44, determine by how many orders of magnitude the quantities differ. Lemon juice with pH = 2.3 and beer with pH = 4.1

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 39-44, determine by how many orders of magnitude the quantities differ. The sound intensities of a riveter at 95 dB and ordinary conversation at 65 dB

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 39-44, determine by how many orders of magnitude the quantities differ. The sound intensities of city traffic at 70 dB and rustling leaves at 10 dB

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Comparing Earthquakes How many times more severe was the 1978 Mexico City earthquake (R=7.9) than the 1994 Los Angeles earthquake (R=6.6)?

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Comparing Earrthquakes How many times more severe was the 1995 Kobe, Japan, earthquake (R=7.2) than the 1994 Los Angeles earthquake (R=6.6)?

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Chemical Acidity The pH of carbonated water is 3.9 and the pH of household ammonia is 11.9. (a) What are their hydrogen-ion concentrations? (b) How many times greater is the hydrogen-ion concentration of carbonated water than that of ammonia? (c) By how many orders of magnitude do the con

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Chemical Acidity Stomach acid has a pH of about 2.0, and blood has a pH of 7.4. (a) What are their hydrogen-ion concentrations? (b) How many times greater is the hydrogen-ion concentration of stomach acid than that of blood? (c) By how many orders of magnitude do the concentrations differ

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Newton's Law of Cooling A cup of coffee has cooled from \(92^{\circ} \mathrm{C}\) to \(50^{\circ} \mathrm{C}\) after 12 min in a room at \(22^{\circ} \mathrm{C}\). How long will the cup take to cool to \(30^{\circ} \mathrm{C}\) ?

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Newton's Law of Cooling A cake is removed from an oven at \(350^{\circ} \mathrm{F}\) and cools to \(120^{\circ} \mathrm{F}\) after 20 min in a room at \(65^{\circ} \mathrm{F}\). How long will the cake take to cool to \(90^{\circ} \mathrm{F}\)?

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Newton's Law of Cooling Experiment A thermometer is removed from a cup of coffee and placed in water with a temperature \(\left(T_m\right)\) of \(10^{\circ} \mathrm{C}\). The data in Table 3.24 were collected over the next 30 sec. (a) Draw

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Newtons Law of Cooling Experiment A thermometer was removed from a cup of hot chocolate and placed in a saline solution with temperature \(T_m=0^\circ \mathrm C\) . The data in Table 3.25 were collected over the next 30 sec. (a) Draw a scatter plot of the data \(T-T_m\) . (b) Find an exponent

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Penicillin Use The use of penicillin became so widespread in the 1980s in Hungary that it became practically useless against common sinus and ear infections. Now the use of more effective antibiotics has caused a decline in penicillin resistance. The bar graph shows the use of penicillin in Hungary f

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Writing to Learn Which regression model would you use for the data in Exercise 53? Discuss various options, and explain why you chose the model you did. Support your writing with tables and graphs as needed.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Writing to Learn In Exercises 5558, tables of (x, y) data pairs are given. Determine whether a linear, logarithmic, exponential, or power regression equation is the best model for the data. Explain your choice. Support your writing with tables and graphs as needed. \(\begin{array}{c|cccc} x & 1 &

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Writing to Learn In Exercises 5558, tables of (x, y) data pairs are given. Determine whether a linear, logarithmic, exponential, or power regression equation is the best model for the data. Explain your choice. Support your writing with tables and graphs as needed. \(\begin{array}{c|cccc} x & 1 &

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Writing to Learn In Exercises 5558, tables of (x, y) data pairs are given. Determine whether a linear, logarithmic, exponential, or power regression equation is the best model for the data. Explain your choice. Support your writing with tables and graphs as needed. \(\begin{array}{c|cccc} x & 1 &

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Writing to Learn In Exercises 5558, tables of (x, y) data pairs are given. Determine whether a linear, logarithmic, exponential, or power regression equation is the best model for the data. Explain your choice. Support your writing with tables and graphs as needed. \(\begin{array}{c|cccc} x & 1 &

Precalculus: Graphical, Numerical, Algebraic 8th Edition
True or False The order of magnitude of a positive number is its natural logarithm. Justify your answer.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
True or False According to Newtons Law of Cooling, an object will approach the temperature of the medium that surrounds it. Justify your answer.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 6164, solve the problem without using a calculator. Multiple Choice Solve \(2^{3 x-1}=32\) (A) x = 1 (B) x = 2 (C) x = 4 (D) x = 11 (E) x = 13

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 6164, solve the problem without using a calculator. Multiple Choice Solve \(\ln x=-1\) (A) x = -1 (B) x = 1/e (C) x = 1 (D) x = e (E) No solution is possible.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 6164, solve the problem without using a calculator. Multiple Choice How many times more severe was the 2001 earthquake in Arequipa, Peru \(\left(R_{1}=8.1\right)\), than the 1998 double earthquake in Takhar province, Afghanistan \(\left(R_{2}=6.1\right)\)? (A) 2

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 6164, solve the problem without using a calculator. Multiple Choice Newtons Law of Cooling is (A) an exponential model. (B) a linear model. (C) a logarithmic model. (D) a logistic model. (E) a power model.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 65 and 66, use the data in Table 3.26. Determine whether a linear, logarithmic, exponential, power, or logistic regression equation is the best model for the data. Explain your choice. Support your writing with tables and graphs as needed. Writing to Learn Modeling Population

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 65 and 66, use the data in Table 3.26. Determine whether a linear, logarithmic, exponential, power, or logistic regression equation is the best model for the data. Explain your choice. Support your writing with tables and graphs as needed. Writing to Learn Modeling Population

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Group Activity Normal Distribution The function \(f(x)=k \cdot e^{-c x^{2}}\), where c and k are positive constants, is a bell-shaped curve that is useful in probability and statistics. (a) Graph f for c = 1 and k = 0.1 , 0.5, 1, 2, 10. Explain the effect of changing k. (b) Graph f for k

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Writing to Learn Prove if \(u / v=10^{n}\) for \(u>0\) and \(v>0\), then log u - log v = n. Explain how this result relates to powers of ten and orders of magnitude.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Potential Energy The potential energy E (the energy stored for use at a later time) between two ions in a certain molecular structure is modeled by the function \(E=-\frac{5.6}{r}+10 e^{-r / 3}\) where r is the distance separating the nuclei. (a) Writing to Learn Graph this functi

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Example 8, the Newtons Law of Cooling model was \(T(t)-T_{m}=\left(T_{0}-T_{m}\right) e^{-k t}=61.656 \times 0.92770^{t}\) Determine the value of k.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Justify the conclusion made about natural logarithmic regression on page 299.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Justify the conclusion made about power regression on page 299.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 7378, solve the equation or inequality. \(e^{x}+x=5\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 7378, solve the equation or inequality. \(e^{2 x}-8 x+1=0\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 7378, solve the equation or inequality. \(e^{x}<5+\ln x\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 7378, solve the equation or inequality. \(\ln |x|-e^{2 x} \geq 3\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 7378, solve the equation or inequality. \(2 \log x-4 \log 3>0\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 7378, solve the equation or inequality. \(2 \log (x+1)-2 \log 6<0\)