1. Review of Algebra

2. Equations & Inequalities

3. Functions & Graphs

4. Polynomial Functions

5. Rational Functions

6. Exponential and Logarithmic Functions

7. Systems of Equations and Inequalities

8. Matrices and Determinants

9. Conic Sections

10. Sequences, Induction, and Probability

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

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

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

Using a calculator to evaluate exponential expressions involving base e

Graph exponential growth functions

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

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) <img src="https://lightcat-files.s3.amazonaws.com/problem_images/310da44985300604-1675890982364.jpg" alt="" />

Finding an Interest Rate to Match Certain Financial Goals, Ex 3

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

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) = 2.2^x

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

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. h(x) = 2^(x+1) – 1

Deriving the Compound Interest Formula

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

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

Use Compound Interest Formulas

Exponential Functions

Compound Interest Example - Find Starting Principal

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

Evaluate Exponential Functions: Base e

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

Transformation of an Exponential Function / Example 14.5

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

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

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

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)

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.

Evaluating an exponential function with base e that models a real world situation

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

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

In Exercises 61–64, give the equation of each exponential function whose graph is shown. <img src="https://lightcat-files.s3.amazonaws.com/problem_images/35852ad21589f816-1675892065917.jpg" alt="" /><img class="fr-dib" src="https://lightcat-files.s3.amazonaws.com/problem_images/0ef937c3aa7ad804-1678176795060.jpg" style="width: 300px;">

In Exercises 61–64, give the equation of each exponential function whose graph is shown. <img src="https://lightcat-files.s3.amazonaws.com/problem_images/0d5ddf9b7bf9a9a7-1677583751071.jpg" alt="" />

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

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

Graph of an Exponential Function

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

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) <img src="https://lightcat-files.s3.amazonaws.com/problem_images/e94785f40a19ab58-1675888511854.jpg" alt="" />

Understanding Simple Interest and Compound Interest

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

Finding an Interest Rate to Match Certain Financial Goals, Ex 1

Evaluate Exponential Functions with Base e

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

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

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

Transformation of an Exponential Function / Example 14.3

Find compound interest using an investment model

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

Finding the Equation of an Exponential Function

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

Graph each function. Give the domain and range. See Example 3. ƒ(x) = -(1/3)^(x-2) + 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(-1.68)

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

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)

Graphing Exponential Functions

Deriving the Annual Compound Interest Formula

Radioactive Decay and Exponential Growth

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

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

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) <img src="https://lightcat-files.s3.amazonaws.com/problem_images/fd087fe7aee9be99-1676959990708.jpg" alt="" />

Exponential Growth / Population Growth Problem.

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. <img src="https://lightcat-files.s3.amazonaws.com/problem_images/5f10c558bc362f89-1671819593011.jpg" alt="" />

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

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

Deriving the Continuous Compounding Formula

Evaluate Exponential Functions at Given Values

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)

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

Identify the Exponential Function

Graph each function. Give the domain and range. See Example 3. ƒ(x) = (1/3)^(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. g(-1.68)

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)

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

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(-3)

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

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

Solving a Continuous Compounding Problem

Transformation of an Exponential Function / Example 14.4

Compound Interest - More than Once Per Year

Graph of y = e ^ (x + 3) using Graph Transformations

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)

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 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

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

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

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

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

Graph exponential decay functions

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

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 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. <img src="https://lightcat-files.s3.amazonaws.com/problem_images/ed6ab88e198af581-1671818346246.jpg" alt="" />

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

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) = 3^x and g(x) = -3^x

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.

Compare exponential models using properties of exponents

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

Evaluating and Graphing Exponential Functions

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)

Graphing Exponential Functions w/ Graph Transformations

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(3/2)

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. 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?

Finding an Interest Rate to Match Certain Financial Goals, Ex 2

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

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