Algebra II: Exponential vs. Power

Objectives

• For positive values of x, students will identify the following behaviors of exponential and power functions:
  • For large (x>a) x-values, exponential functions of the form y =a^x grow faster than power functions of the form = x^a
  • For particular x-values, power and exponential functions can be equivalent
  • On certain intervals, power functions can have greater value than exponential functions

Vocabulary

• Exponential function
• Power function
• Exponent
• Base

About the Lesson

This lesson involves comparing rates of growth between the exponential function f(x)=a^x and the power function g(x)=x^a for positive x-values. As a result, students will:

• Compare the discrete value of these functions for a = 2, 3, 4, and 5 as x moves along a number line from 1 to 5.
• Compare the graphs of the functions for a = 2, 3, 4, and 5 as x moves along the x-axis.