Education Technology

# Activities

• ##### Subject Area

• Math: Algebra II: Logarithms and Exponentials

9-12

45 Minutes

• ##### Device
• TI-Nspire™ CX/CX II
• TI-Nspire™ CX CAS/CX II CAS
• TI-Nspire™ Navigator™
• ##### Software

TI-Nspire™ CX
TI-Nspire™ CX CAS

5.0

## Exponential vs. Power

#### Activity Overview

Compare rates of growth between an exponential function and a power function for positive x-values.

#### 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 =ax grow faster than power functions of the form = xa
• 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)=ax and the power function g(x)=xa 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.