Precalculus: Graphical, Numerical, Algebraic 8th Edition solutions

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Exercise numbers with a gray background indicate problems that the authors have designed to be solved without a calculator. In Exercises 14, evaluate the expression without using a calculator. \(\text { 1. } \sqrt[3]{-216}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Exercise numbers with a gray background indicate problems that the authors have designed to be solved without a calculator. In Exercises 14, evaluate the expression without using a calculator. \(\text { 2. } \sqrt[3]{\frac{125}{8}}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Exercise numbers with a gray background indicate problems that the authors have designed to be solved without a calculator. In Exercises 14, evaluate the expression without using a calculator. \(\text { 3. } 27^{2 / 3}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Exercise numbers with a gray background indicate problems that the authors have designed to be solved without a calculator. In Exercises 14, evaluate the expression without using a calculator. \(\text { 4. } 4^{5 / 2}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 58, rewrite the expression using a single positive exponent. \(\text { 5. }\left(2^{-3}\right)^{4}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 58, rewrite the expression using a single positive exponent. \(\text { 6. }\left(3^{4}\right)^{-2}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 58, rewrite the expression using a single positive exponent. \(\text { 7. }\left(a^{-2}\right)^{3}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 58, rewrite the expression using a single positive exponent. \(\text { 8. }\left(b^{-3}\right)^{-5}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 910, use a calculator to evaluate the expression. \(\text { 9. } \sqrt[5]{-5.37824}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 910, use a calculator to evaluate the expression. \(\text { 10. } \sqrt[4]{92.3521}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 16, which of the following are exponential functions? For those that are exponential functions, state the initial value and the base. For those that are not, explain why not. \(\text { 1. } y=x^{8}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 16, which of the following are exponential functions? For those that are exponential functions, state the initial value and the base. For those that are not, explain why not. \(\text { 2. } y=3^{x}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 16, which of the following are exponential functions? For those that are exponential functions, state the initial value and the base. For those that are not, explain why not. \(\text { 3. } y=5^{x}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 16, which of the following are exponential functions? For those that are exponential functions, state the initial value and the base. For those that are not, explain why not. \(\text { 4. } y=4^{2}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 16, which of the following are exponential functions? For those that are exponential functions, state the initial value and the base. For those that are not, explain why not. \(\text { 5. } y=x^{\sqrt{x}}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 16, which of the following are exponential functions? For those that are exponential functions, state the initial value and the base. For those that are not, explain why not. \(\text { 6. } y=x^{1.3}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 710, compute the exact value of the function for the given x-value without using a calculator. \(\text { 7. } f(x)=3 \cdot 5^{x} \text { for } x=0\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 710, compute the exact value of the function for the given x-value without using a calculator. \(\text { 8. } f(x)=6 \cdot 3^{x} \text { for } x=-2\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 710, compute the exact value of the function for the given x-value without using a calculator. \(\text { 9. } f(x)=-2 \cdot 3^{x} \text { for } x=1 / 3\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 710, compute the exact value of the function for the given x-value without using a calculator. \(\text { 10. } f(x)=8 \cdot 4^{x} \text { for } x=-3 / 2\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 11 and 12, determine a formula for the exponential func- tion whose values are given in Table 3.6. \(\text { 11. } f(x)\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 11 and 12, determine a formula for the exponential func- tion whose values are given in Table 3.6. \(\text { 12. } g(x)\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 13 and 14, determine a formula for the exponential func- tion whose graph is shown in the figure. \(\text { 13. } f(x)\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 13 and 14, determine a formula for the exponential func- tion whose graph is shown in the figure. \(\text { 14. } g(x)\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1524, describe how to transform the graph of into the graph of g. Sketch the graphs by hand and support your answer with a grapher. \(\text { 15. } f(x)=2^{x}, g(x)=2^{x-3}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1524, describe how to transform the graph of into the graph of g. Sketch the graphs by hand and support your answer with a grapher. \(\text { 16. } f(x)=3^{x}, g(x)=3^{x+4}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1524, describe how to transform the graph of into the graph of g. Sketch the graphs by hand and support your answer with a grapher. \(\text { 17. } f(x)=4^{x}, g(x)=4^{-x}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1524, describe how to transform the graph of into the graph of g. Sketch the graphs by hand and support your answer with a grapher. \(\text { 18. } f(x)=2^{x}, g(x)=2^{5-x}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1524, describe how to transform the graph of into the graph of g. Sketch the graphs by hand and support your answer with a grapher. \(\text { 19. } f(x)=0.5^{x}, g(x)=3 \cdot 0.5^{x}+4\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1524, describe how to transform the graph of into the graph of g. Sketch the graphs by hand and support your answer with a grapher. \(\text { 20. } f(x)=0.6^{x}, g(x)=2 \cdot 0.6^{3 x}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1524, describe how to transform the graph of into the graph of g. Sketch the graphs by hand and support your answer with a grapher. \(\text { 21. } f(x)=e^{x}, g(x)=e^{-2 x}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1524, describe how to transform the graph of into the graph of g. Sketch the graphs by hand and support your answer with a grapher. \(\text { 22. } f(x)=e^{x}, g(x)=-e^{-3 x}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1524, describe how to transform the graph of into the graph of g. Sketch the graphs by hand and support your answer with a grapher. \(\text { 23. } f(x)=e^{x}, g(x)=2 e^{3-3 x}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1524, describe how to transform the graph of into the graph of g. Sketch the graphs by hand and support your answer with a grapher. \(\text { 24. } f(x)=e^{x}, g(x)=3 e^{2 x}-1\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2530, (a) match the given function with its graph. (b) Writing to Learn Explain how to make the choice without using a grapher. \(\text { 25. } y=3^{x}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2530, (a) match the given function with its graph. (b) Writing to Learn Explain how to make the choice without using a grapher. \9\text { 26. } y=2^{-x}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2530, (a) match the given function with its graph. (b) Writing to Learn Explain how to make the choice without using a grapher. \(\text { 27. } y=-2^{x}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2530, (a) match the given function with its graph. (b) Writing to Learn Explain how to make the choice without using a grapher. \(\text { 28. } y=-0.5^{x}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2530, (a) match the given function with its graph. (b) Writing to Learn Explain how to make the choice without using a grapher. \(\text { 29. } y=3^{-x}-2\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2530, (a) match the given function with its graph. (b) Writing to Learn Explain how to make the choice without using a grapher. \(\text { 30. } y=1.5^{x}-2\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 3134, state whether the function is an exponential growth function or exponential decay function, and describe its end behavior using limits. \(\text { 31. } f(x)=3^{-2 x}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 3134, state whether the function is an exponential growth function or exponential decay function, and describe its end behavior using limits. \(\text { 32. } f(x)=\left(\frac{1}{e}\right)^{x}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 3134, state whether the function is an exponential growth function or exponential decay function, and describe its end behavior using limits. \(\text { 33. } f(x)=0.5^{x}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 3134, state whether the function is an exponential growth function or exponential decay function, and describe its end behavior using limits. \(\text { 34. } f(x)=0.75^{-x}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 3538, solve the inequality graphically. \(\text { 35. } 9^{x}<4^{x}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 3538, solve the inequality graphically. \(\text { 36. } 6^{-x}>8^{-x}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 3538, solve the inequality graphically. \(\text { 37. }\left(\frac{1}{4}\right)^{x}>\left(\frac{1}{3}\right)^{x}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 3538, solve the inequality graphically. \(\text { 38. }\left(\frac{1}{3}\right)^{x}<\left(\frac{1}{2}\right)^{x}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 39 and 40, use the properties of exponents to prove that two of the given three exponential functions are identical. Support graphically. \(\begin{array}{l}\text{(a) } y_{1}=3^{2 x+4}\\\text{(b) } y_{2}=3^{2 x}+4\\\text{(c) } y_{3}=9^{x+2}\end{array}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 39 and 40, use the properties of exponents to prove that two of the given three exponential functions are identical. Support graphically. \(\begin{array}{l}\text{(a) } y_{1}=4^{3 x-2}\\\text{(b) } y_{2}=2\left(2^{3 x-2}\right)\\\text{(c) } y_{3}=2^{3 x-1}\end{array}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 4144, use a grapher to graph the function. Find the y-intercept and the horizontal asymptotes. \(\text { 41. } f(x)=\frac{12}{1+2 \cdot 0.8^{x}}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 4144, use a grapher to graph the function. Find the y-intercept and the horizontal asymptotes. \(\text { 42. } f(x)=\frac{18}{1+5 \cdot 0.2^{x}}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 4144, use a grapher to graph the function. Find the y-intercept and the horizontal asymptotes. \(\text { 43. } f(x)=\frac{16}{1+3 e^{-2 x}}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 4144, use a grapher to graph the function. Find the y-intercept and the horizontal asymptotes. \(\text { 44. } g(x)=\frac{9}{1+2 e^{-x}}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 4550, graph the function and analyze it for domain, range, continuity, increasing or decreasing behavior, symmetry, boundedness, extrema, asymptotes, and end behavior. \(f(x)=3 \cdot 2^{x}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 4550, graph the function and analyze it for domain, range, continuity, increasing or decreasing behavior, symmetry, boundedness, extrema, asymptotes, and end behavior. \(f(x)=4 \cdot 0.5^{x}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 4550, graph the function and analyze it for domain, range, continuity, increasing or decreasing behavior, symmetry, boundedness, extrema, asymptotes, and end behavior. \(f(x)=4 \cdot e^{3 x}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 4550, graph the function and analyze it for domain, range, continuity, increasing or decreasing behavior, symmetry, boundedness, extrema, asymptotes, and end behavior. \(f(x)=5 \cdot e^{-x}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 4550, graph the function and analyze it for domain, range, continuity, increasing or decreasing behavior, symmetry, boundedness, extrema, asymptotes, and end behavior. \(f(x)=\frac{5}{1+4 \cdot e^{-2 x}}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 4550, graph the function and analyze it for domain, range, continuity, increasing or decreasing behavior, symmetry, boundedness, extrema, asymptotes, and end behavior. \(f(x)=\frac{6}{1+2 \cdot e^{-x}}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Using the midyear data in Table 3.7 and assuming the growth is exponential, when did the population of Austin surpass 800,000 persons?

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Population Growth Using the data in Table 3.7 and assuming the growth is exponential, when would the population of Columbus surpass 800,000 persons?

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Population Growth Using the data in Table 3.7 and assuming the growth is exponential, when were the populations of Austin and Columbus equal?

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Population Growth Using the data in Table 3.7 and assuming the growth is exponential, which cityAustin or Columbuswould reach a population of 1 million first, and in what year?

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Population Growth Using 20th-century U.S. census data, the population of Ohio can be modeled by \(P(t)=\frac{12.79}{1+2.402 e^{-0.0309 x}}\) where P is the population in millions and t is the number of years since April 1, 1900. Based on this model, when was the population of Ohio 10 mil

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Population Growth Using 20th-century U.S. census data, the population of New York state can be modeled by \(P(t)=\frac{19.875}{1+57.993 e^{-0.035005 t}}\) where P is the population in millions and t is the number of years since 1800. Based on this model, (a) What was the population of New

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Bacteria Growth The number B of bacteria in a petridish culture after t hours is given by \(B=100 e^{0.693 t}\) . (a) What was the initial number of bacteria present? (b) How many bacteria are present after 6 hours?

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Carbon Dating The amount C in grams of carbon-14 present in a certain substance after t years is given by \(C=20 e^{-0.0001216 t}\) . (a) What was the initial amount of carbon-14 present? (b) How much is left after 10,400 years? When will the amount left be 10 g?

Precalculus: Graphical, Numerical, Algebraic 8th Edition
True or False Every exponential function is strictly in- creasing. Justify your answer.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
True or False Every logistic growth function has two horizontal asymptotes. Justify your answer.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 6164, solve the problem without using a calculator. Multiple Choice Which of the following functions is exponential?

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 6164, solve the problem without using a calculator. Multiple Choice What point do all functions of the form ??\(f(x)=b^{x}(b>0)\) have in common?

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 6164, solve the problem without using a calculator. Multiple Choice The growth factor for \(f(x)=4 \cdot 3^{x}\) is

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 6164, solve the problem without using a calculator. Multiple Choice For \(x>0\), which of the following is true?

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Graph each function and analyze it for domain, range, increas- ing or decreasing behavior, boundedness, extrema, asymptotes, and end behavior. \(\text { (a) } f(x)=x \cdot e^{x}\) \(\text { (b) } g(x)=\frac{e^{-x}}{x}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Use the properties of exponents to solve each equation. Support graphically. \(\text { (a) } 2^{x}=4^{2}\) \(??\text { (b) } 3^{x}=27\) \(\text { (c) } 8^{x / 2}=4^{x+1}\) \(\text { (d) } 9^{x}=3^{x+1}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Writing to Learn Table 3.8 gives function values for \(y=f(x) \text { and } y=g(x)\). Also, three different graphs are shown. 1. Which curve of those shown in the graph most closely resembles the graph of \(y=f(x)\) ? Explain your choice. 2. Which curve most closely resembles the graph of

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Writing to Learn Let \(f(x)=2^{x}\). Explain why the graph of \(f(a x+b)\) can be obtained by applying one transformation to the graph of \(y=c^{x}\) for an appropriate value of c. What is c?

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Exercises 6972 refer to the expression \(f(a, b, c)=a \cdot b^{c}\). For example, if a = 2, b = 3, and c = x, the expression is \(f(2,3, x)=2 \cdot 3^{x}\), an exponential function. If b = x, state conditions on a and c under which the expression \(f(a, b, c)\) is a quadratic power function.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Exercises 6972 refer to the expression \(f(a, b, c)=a \cdot b^{c}\). For example, if a = 2, b = 3, and c = x, the expression is \(f(2,3, x)=2 \cdot 3^{x}\), an exponential function. If b = x, state conditions on a and c under which the expression \(f(a, b, c)\) is a decreasing linear function.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Exercises 6972 refer to the expression \(f(a, b, c)=a \cdot b^{c}\). For example, if a = 2, b = 3, and c = x, the expression is \(f(2,3, x)=2 \cdot 3^{x}\), an exponential function. If c = x, state conditions on a and c under which the expression \(f(a, b, c)\) is an increasing exponential functi

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Exercises 6972 refer to the expression \(f(a, b, c)=a \cdot b^{c}\). For example, if a = 2, b = 3, and c = x, the expression is \(f(2,3, x)=2 \cdot 3^{x}\), an exponential function. If c = x, state conditions on a and c under which the expression \(f(a, b, c)\) is a decreasing exponential funct

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Prove that for constants a, b, and c, with \(a>0,0<b<1, \text { and } c>0\).