1. Lesson 7-6: Exponential Functions

2. Students will be able to evaluate and graph exponential functions.
Objectives
Students will be able to evaluate and graph exponential functions.

3. Exponential Functions
An exponential function is a function of the form y = a ∙ bx where a ≠ 0, b > 0, b ≠ 1, and x is a real number.

4. Problem 1: Identifying Linear and Exponential Functions
Suppose all the x-values in a table have a common difference. If all the y-values have a common difference, then the table represents an arithmetic sequence, or a linear function.
If all of the y-values have a common ratio, then the table represents a geometric sequence, which is an exponential function.

5. Problem 2: Evaluating an Exponential Function
Suppose 30 flour beetles are left undisturbed in a warehouse bin. The beetle population doubles each week. The function f(x) = 30 ∙ 2x gives the population after x weeks. How many beetles will there be after 56 days?

6. Problem 3: Graphing an Exponential Function
What is the graph of y = 3 ∙ 2x ?
Make a table of x- and y-values. Then plot the ordered pairs on a coordinate plane.

7. Problem 4: Graphing an Exponential Model
Computer mapping software allows you to zoom in on an area to view it in more detail. The function f(x) = 100 ∙ 0.25x models the percent of the original area the map shows after zooming in x times. Graph the function.