Section 8 – 7 Exponential Functions

Objectives:To evaluate exponential functions

To graph exponential functions

Exponential FunctionA function in the form , where a is a

nonzero constant, b is greater than 0 and not equal to 1, and x is a real number.

Examples

Example 1 Evaluating an Exponential Function

Evaluate each exponential function.

A) for x = 2, 3, 4

B) for the domain {-3, 6}

Evaluate each exponential function for the domain {-2, 0, 3}.

Example 2 Real-World Problem Solving

A) Suppose 20 rabbits are taken to an island. The rabbit population then triples every half year. The function , where x is the number of half year periods, models this situation. How many rabbits would there be after 2 years?

B) Suppose 10 animals are taken to an island. The population quadruples every year. The function , where x is the number of years, models this situation. How many animals would there be after 6 years?

C) Suppose an investment of $10,000 doubles in value every 13 years. How much is the investment worth after 52 years?

D) Suppose an investment of $5,000 doubles in value every 12 years. How much is the investment worth after 24 years?

Homework:

• Textbook Page 432; #1 – 11

Section 8 – 7 Continued…

Objectives:To graph exponential functions

The Graphs of Exponential Functions

Example 3 Graphs of Exponential Functions

A) Graph

B) Graph

C) Graph

D) Graph

Example 4 Real-World Problem Solving

A) Suppose 2 mice live in a barn. The number of mice quadruples every month. Write an exponential function to model the population growth. Graph the

function.

B) Many photocopiers allow you to choose how large you want an image to be. The function models the new size of an image being copied over and over

at 150%, where x is the number of enlargements. Graph the function.

Homework

Textbook Page 432 – 433; #12 – 24 All