Lesson 7-6: Exponential Functions

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

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.

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.

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?

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.

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.