Introduction to Exponential Functions

Multiple Choice

Determine if the function is an exponential function.

If so, identify the power & base, then evaluate for $x=4$ .

$f\left(x\right)=\left(-2\right)^{x}$

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Multiple Choice

Determine if the function is an exponential function.

If so, identify the power & base, then evaluate for $x=4$ .

$f\left(x\right)=3\left(1.5\right)^{x}$

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Multiple Choice

Determine if the function is an exponential function.

If so, identify the power & base, then evaluate for $x=4$ .

$f\left(x\right)=\left(\frac12\right)^{x}$

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Textbook Question

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

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Textbook Question

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

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Textbook Question

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.

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Textbook Question

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

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Textbook Question

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

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Textbook Question

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

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Textbook Question

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

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Textbook Question

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?

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Textbook Question

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

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Textbook Question

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

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Textbook Question

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)

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Textbook Question

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

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Textbook Question

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)

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Textbook Question

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)

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Textbook Question

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)

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Textbook Question

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)

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Textbook Question

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)

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Textbook Question

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

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Textbook Question

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

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Textbook Question

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

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Textbook Question

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

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Textbook Question

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

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Textbook Question

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

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Textbook Question

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

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Textbook Question

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

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Textbook Question

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

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Textbook Question

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

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Textbook Question

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

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Textbook Question

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.

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Textbook Question

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.

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Textbook Question

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.

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Textbook Question

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?

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Textbook Question

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

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Textbook Question

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

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Textbook Question

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

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Textbook Question

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

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Textbook Question

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

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Textbook Question

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

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Textbook Question

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

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