6. Exponential and Logarithmic Functions

In Exercises 1–10, approximate each number using a calculator. Round your answer to three decimal places. 2^3.4

Fill in the blank(s) to correctly complete each sentence. If ƒ(x) = 4^x, then ƒ(2) = and ƒ(-2) = ________.

In Exercises 1–4, the graph of an exponential function is given. Select the function for each graph from the following options: f(x) = 4^x, g(x) = 4^-x, h(x) = -4^(-x), r(x) = -4^(-x)+3 3.

In Exercises 1–10, approximate each number using a calculator. Round your answer to three decimal places. 4^-1.5

In Exercises 1–10, approximate each number using a calculator. Round your answer to three decimal places. e^2.3

In Exercises 5–9, graph f and g in the same rectangular coordinate system. Use transformations of the graph of f to obtain the graph of g. Graph and give equations of all asymptotes. Use the graphs to determine each function's domain and range. f(x) = 3^x and g(x) = -3^x

Solve each equation. Round answers to the nearest hundredth as needed. x^(2/3) =36

Use the compound interest formulas to solve Exercises 10–11. Suppose that you have $5000 to invest. Which investment yields the greater return over 5 years: 1.5% compounded semiannually or 1.45% compounded monthly?

In Exercises 11–18, graph each function by making a table of coordinates. If applicable, use a graphing utility to confirm your hand-drawn graph. f(x) = 4^x

In Exercises 11–18, graph each function by making a table of coordinates. If applicable, use a graphing utility to confirm your hand-drawn graph. g(x) = (3/2)^x

For ƒ(x) = 3^x and g(x)= (1/4)^x find each of the following. Round answers to the nearest thousandth as needed. See Example 1. g(2)

In Exercises 11–18, graph each function by making a table of coordinates. If applicable, use a graphing utility to confirm your hand-drawn graph. f(x) = (0.6)^x

In Exercises 19–24, the graph of an exponential function is given. Select the function for each graph from the following options: f(x) = 3^x, g(x) = 3^(x-1), h(x) = 3^x - 1 ; f(x) = -3^x, G(x) = 3^(-x), H(x) = -3^(-x)

For ƒ(x) = 3^x and g(x)= (1/4)^x find each of the following. Round answers to the nearest thousandth as needed. See Example 1. g(3/2)

In Exercises 19–24, the graph of an exponential function is given. Select the function for each graph from the following options: f(x) = 3^x, g(x) = 3^(x-1), h(x) = 3^x - 1 ; f(x) = -3^x, G(x) = 3^(-x), H(x) = -3^(-x)

In Exercises 25-34, begin by graphing f(x) = 2^x. Then use transformations of this graph to graph the given function. Be sure to graph and give equations of the asymptotes. Use the graphs to determine each function's domain and range. If applicable, use a graphing utility to confirm your hand-drawn graphs. g(x) = 2^(x+1)

For ƒ(x) = 3^x and g(x)= (1/4)^x find each of the following. Round answers to the nearest thousandth as needed. See Example 1. g(-1.68)

In Exercises 25-34, begin by graphing f(x) = 2^x. Then use transformations of this graph to graph the given function. Be sure to graph and give equations of the asymptotes. Use the graphs to determine each function's domain and range. If applicable, use a graphing utility to confirm your hand-drawn graphs. h(x) = 2^(x+1) – 1

Graph each function. See Example 2. ƒ(x) = (1/3)^x

In Exercises 25-34, begin by graphing f(x) = 2^x. Then use transformations of this graph to graph the given function. Be sure to graph and give equations of the asymptotes. Use the graphs to determine each function's domain and range. If applicable, use a graphing utility to confirm your hand-drawn graphs. g(x) = −2^x

Graph each function. See Example 2. ƒ(x) = 4^-x

The figure shows the graph of f(x) = e^x. In Exercises 35-46, use transformations of this graph to graph each function. Be sure to give equations of the asymptotes. Use the graphs to determine graphs. each function's domain and range. If applicable, use a graphing utility to confirm your hand-drawn g(x) = e^x+2

The figure shows the graph of f(x) = e^x. In Exercises 35-46, use transformations of this graph to graph each function. Be sure to give equations of the asymptotes. Use the graphs to determine graphs. each function's domain and range. If applicable, use a graphing utility to confirm your hand-drawn h(x) = e^(x-1)+2

The figure shows the graph of f(x) = e^x. In Exercises 35-46, use transformations of this graph to graph each function. Be sure to give equations of the asymptotes. Use the graphs to determine graphs. each function's domain and range. If applicable, use a graphing utility to confirm your hand-drawn g(x) = 2e^x

The figure shows the graph of f(x) = e^x. In Exercises 35-46, use transformations of this graph to graph each function. Be sure to give equations of the asymptotes. Use the graphs to determine graphs. each function's domain and range. If applicable, use a graphing utility to confirm your hand-drawn h(x) = e^2x + 1

In Exercises 47–52, graph functions f and g in the same rectangular coordinate system. Graph and give equations of all asymptotes. If applicable, use a graphing utility to confirm your hand-drawn graphs. f(x) = 3^x and g(x) = (1/3). 3^x

Graph each function. Give the domain and range. See Example 3. ƒ(x) = 2^(x+2) - 4

In Exercises 47–52, graph functions f and g in the same rectangular coordinate system. Graph and give equations of all asymptotes. If applicable, use a graphing utility to confirm your hand-drawn graphs. f(x) = (½)^x and g(x) = (1/2)^(x-1) + 1

Use the compound interest formulas A = P (1+ r/n)^nt and A =Pe^rt to solve exercises 53-56. Round answers to the nearest cent. Find the accumulated value of an investment of $10,000 for 5 years at an interest rate of 1.32% if the money is a. compounded semiannually; b. compounded quarterly; c. compounded monthly; d. compounded continuously.

Use the compound interest formulas A = P (1+ r/n)^nt and A =Pe^rt to solve exercises 53-56. Round answers to the nearest cent. Find the accumulated value of an investment of $10,000 for 5 years at an interest rate of 1.32% if the money is a. compounded semiannually; b. compounded quarterly; c. compounded monthly; d. compounded continuously.

Use the compound interest formulas A = P (1+ r/n)^nt and A =Pe^rt to solve exercises 53-56. Round answers to the nearest cent. Find the accumulated value of an investment of $10,000 for 5 years at an interest rate of 1.32% if the money is a. compounded semiannually; b. compounded quarterly; c. compounded monthly; d. compounded continuously.

Use the compound interest formulas A = P (1+ r/n)^nt and A =Pe^rt to solve exercises 53-56. Round answers to the nearest cent. Suppose that you have $12,000 to invest. Which investment yields the greater return over 3 years: 0.96% compounded monthly or 0.95% compounded continuously?

Graph each function. Give the domain and range. See Example 3. ƒ(x) = (1/3)^(-x+1)

Graph y= 2^x and x = 2^y in the same rectangular coordinate system.

Graph each function. Give the domain and range. See Example 3. ƒ(x) = -(1/3)^(x+2) - 1

Solve each equation. See Examples 4–6. 4^(x-2) = 2^(3x+3)

Graph f(x) = 2^x and its inverse function in the same rectangular coordinate system.

Solve each equation. See Examples 4–6. (√2)^(x+4) = 4^x

Concept Check. If ƒ(x) = a^x and ƒ(3) = 27, determine each function value. ƒ(-1)

In Exercises 1–4, the graph of an exponential function is given. Select the function for each graph from the following options: f(x) = 4^x, g(x) = 4^-x, h(x) = -4^(-x), r(x) = -4^(-x)+3 1.

In Exercises 1–10, approximate each number using a calculator. Round your answer to three decimal places. 3^√5

Solve each equation. Round answers to the nearest hundredth as needed. (1/4)^x=64

In Exercises 1–10, approximate each number using a calculator. Round your answer to three decimal places. e^-0.95

In Exercises 5–9, graph f and g in the same rectangular coordinate system. Use transformations of the graph of f to obtain the graph of g. Graph and give equations of all asymptotes. Use the graphs to determine each function's domain and range. f(x) = e^x and g(x) = 2e^(x/2)

In Exercises 11–18, graph each function by making a table of coordinates. If applicable, use a graphing utility to confirm your hand-drawn graph. f(x) = 4^x

For ƒ(x) = 3^x and g(x)= (1/4)^x find each of the following. Round answers to the nearest thousandth as needed. See Example 1. ƒ(-2)

In Exercises 11–18, graph each function by making a table of coordinates. If applicable, use a graphing utility to confirm your hand-drawn graph. h(x) = (1/2)^x

For ƒ(x) = 3^x and g(x)= (1/4)^x find each of the following. Round answers to the nearest thousandth as needed. See Example 1. ƒ(-5/2)

In Exercises 19–24, the graph of an exponential function is given. Select the function for each graph from the following options: f(x) = 3^x, g(x) = 3^(x-1), h(x) = 3^x - 1 ; f(x) = -3^x, G(x) = 3^(-x), H(x) = -3^(-x)

For ƒ(x) = 3^x and g(x)= (1/4)^x find each of the following. Round answers to the nearest thousandth as needed. See Example 1. ƒ(-1.68)

In Exercises 25-34, begin by graphing f(x) = 2^x. Then use transformations of this graph to graph the given function. Be sure to graph and give equations of the asymptotes. Use the graphs to determine each function's domain and range. If applicable, use a graphing utility to confirm your hand-drawn graphs. g(x) = 2^x – 1

Graph each function. See Example 2. ƒ(x) = 3^x

In Exercises 25-34, begin by graphing f(x) = 2^x. Then use transformations of this graph to graph the given function. Be sure to graph and give equations of the asymptotes. Use the graphs to determine each function's domain and range. If applicable, use a graphing utility to confirm your hand-drawn graphs. g(x) = 2.2^x

Graph each function. See Example 2. ƒ(x) = (1/10)^-x

The figure shows the graph of f(x) = e^x. In Exercises 35-46, use transformations of this graph to graph each function. Be sure to give equations of the asymptotes. Use the graphs to determine graphs. each function's domain and range. If applicable, use a graphing utility to confirm your hand-drawn g(x) = e^x-1

The figure shows the graph of f(x) = e^x. In Exercises 35-46, use transformations of this graph to graph each function. Be sure to give equations of the asymptotes. Use the graphs to determine graphs. each function's domain and range. If applicable, use a graphing utility to confirm your hand-drawn h(x) = e^-x

In Exercises 47–52, graph functions f and g in the same rectangular coordinate system. Graph and give equations of all asymptotes. If applicable, use a graphing utility to confirm your hand-drawn graphs. f(x) = 3^x and g(x) = 3^-x

Graph each function. Give the domain and range. See Example 3. ƒ(x) = 2^(x+3) +1

Use the compound interest formulas A = P (1+ r/n)^nt and A =Pe^rt to solve exercises 53-56. Round answers to the nearest cent. Find the accumulated value of an investment of $10,000 for 5 years at an interest rate of 1.32% if the money is a. compounded semiannually; b. compounded quarterly; c. compounded monthly; d. compounded continuously.

Graph each function. Give the domain and range. See Example 3. ƒ(x) = (1/3)^(x+2)

Use the compound interest formulas A = P (1+ r/n)^nt and A =Pe^rt to solve exercises 53-56. Round answers to the nearest cent. Find the accumulated value of an investment of $10,000 for 5 years at an interest rate of 1.32% if the money is a. compounded semiannually; b. compounded quarterly; c. compounded monthly; d. compounded continuously.

Graph each function. Give the domain and range. See Example 3. ƒ(x) = -(1/3)^(x-2) + 2

In Exercises 61–64, give the equation of each exponential function whose graph is shown.

In Exercises 61–64, give the equation of each exponential function whose graph is shown.

Solve each equation. See Examples 4–6. (5/2)^x = 4/25

Solve each equation. See Examples 4–6. x^5/2 = 32

Solve each equation. See Examples 4–6. (1/e)^-x = (1/e^2)^(x+1)

In Exercises 1–10, approximate each number using a calculator. Round your answer to three decimal places. 2^3.4

In Exercises 1–10, approximate each number using a calculator. Round your answer to three decimal places. 3^√5

Fill in the blank(s) to correctly complete each sentence. The graph of ƒ(x) = -(1/3)^(x+4)-5 is that of ƒ(x) = (1/3)^x reflected across the ______ -axis, translated to the left ______ units and down _______ units.

In Exercises 5–9, graph f and g in the same rectangular coordinate system. Use transformations of the graph of f to obtain the graph of g. Graph and give equations of all asymptotes. Use the graphs to determine each function's domain and range. f(x) = 3^x and g(x) = -3^x

In Exercises 5–9, graph f and g in the same rectangular coordinate system. Use transformations of the graph of f to obtain the graph of g. Graph and give equations of all asymptotes. Use the graphs to determine each function's domain and range. f(x) = e^x and g(x) = 2e^(x/2)

For ƒ(x) = 3^x and g(x)= (1/4)^x find each of the following. Round answers to the nearest thousandth as needed. See Example 1. ƒ(2)

In Exercises 11–18, graph each function by making a table of coordinates. If applicable, use a graphing utility to confirm your hand-drawn graph. h(x) = (1/2)^x

For ƒ(x) = 3^x and g(x)= (1/4)^x find each of the following. Round answers to the nearest thousandth as needed. See Example 1. g(3)

For ƒ(x) = 3^x and g(x)= (1/4)^x find each of the following. Round answers to the nearest thousandth as needed. See Example 1. g(-3)

In Exercises 19–24, the graph of an exponential function is given. Select the function for each graph from the following options: f(x) = 3^x, g(x) = 3^(x-1), h(x) = 3^x - 1 ; f(x) = -3^x, G(x) = 3^(-x), H(x) = -3^(-x)

For ƒ(x) = 3^x and g(x)= (1/4)^x find each of the following. Round answers to the nearest thousandth as needed. See Example 1. g(-5/2)

For ƒ(x) = 3^x and g(x)= (1/4)^x find each of the following. Round answers to the nearest thousandth as needed. See Example 1. g(2.34)

In Exercises 25-34, begin by graphing f(x) = 2^x. Then use transformations of this graph to graph the given function. Be sure to graph and give equations of the asymptotes. Use the graphs to determine each function's domain and range. If applicable, use a graphing utility to confirm your hand-drawn graphs. g(x) = −2^x

Graph each function. See Example 2. ƒ(x) = (3/2)^x

In Exercises 25-34, begin by graphing f(x) = 2^x. Then use transformations of this graph to graph the given function. Be sure to graph and give equations of the asymptotes. Use the graphs to determine each function's domain and range. If applicable, use a graphing utility to confirm your hand-drawn graphs. g(x) = 2.2^x

Graph each function. See Example 2. ƒ(x) = 2^(|x|)

The figure shows the graph of f(x) = e^x. In Exercises 35-46, use transformations of this graph to graph each function. Be sure to give equations of the asymptotes. Use the graphs to determine graphs. each function's domain and range. If applicable, use a graphing utility to confirm your hand-drawn h(x) = e^-x

In Exercises 47–52, graph functions f and g in the same rectangular coordinate system. Graph and give equations of all asymptotes. If applicable, use a graphing utility to confirm your hand-drawn graphs. f(x) = 3^x and g(x) = 3^-x

Graph each function. Give the domain and range. See Example 3. ƒ(x) = (1/3)^x - 2

Use the compound interest formulas A = P (1+ r/n)^nt and A =Pe^rt to solve exercises 53-56. Round answers to the nearest cent. Find the accumulated value of an investment of $10,000 for 5 years at an interest rate of 1.32% if the money is a. compounded semiannually; b. compounded quarterly; c. compounded monthly; d. compounded continuously.

In Exercises 57–58, graph f and g in the same rectangular coordinate system. Then find the point of intersection of the two graphs. f(x) = 2^x, g(x) = 2^-x

Graph each function. Give the domain and range. See Example 3. ƒ(x) = (1/3)^-x

Solve each equation. See Examples 4–6. 4^x = 2

Solve each equation. See Examples 4–6. x^2/3 = 4

Solve each equation. See Examples 4–6. 1/27 = x^-3

Concept Check. If ƒ(x) = a^x and ƒ(3) = 27, determine each function value. ƒ(2)