5. Exponential and Logarithmic Functions

Use Compound Interest Formulas

Exponential Functions

Understanding Simple Interest and Compound Interest

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

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

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

Compound Interest Example - Find Starting Principal

Evaluate Exponential Functions: Base e

Transformation of an Exponential Function / Example 14.5

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

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

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;">

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

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="" />

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

Evaluate Exponential Functions with Base e

Transformation of an Exponential Function / Example 14.3

Find compound interest using an investment model

Finding the Equation of an Exponential Function

Graphing Exponential Functions

Deriving the Annual Compound Interest Formula

Radioactive Decay and Exponential Growth

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

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

Identify the Exponential Function

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

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

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) = 2e^x

Graph exponential decay functions

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="" />

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

Compare exponential models using properties of exponents

Evaluating and Graphing Exponential Functions

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)

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

Learn the toughest concepts covered in Algebra with step-by-step video tutorials and practice problems by world-class tutors

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1. Fundamental Concepts of Algebra

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Expand Logarithmic Expressions

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The Change-of-Base Property

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Use Like Bases to Solve Exponential Equations

Use Logarithms to Solve Exponential Equations

Use the Definition of a Logarithm to Solve Logarithmic Equations

Use the One-to-One Property of Logarithms to Solve Equations

Solve Problems Using Exponential and Logarithmic Equations

Exponential and Logarithmic Equations

Evaluate & Graph Exponential Functions

Evaluate Functions with Base e

Model Exponential Growth and Decay

Use Logistic Growth Models

Choose an Appropriate Model for Data

Express an Exponential Model in Base e

Exponential Growth and Decay

Change From Logarithmic to Exponential Form

Change From Exponential to Logarithmic Form

Evaluate Logarithms

Use Basic Logarithmic Properties

Graph Logarithmic Functions

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Logarithmic Functions

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