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    • Math: Precalculus: Exponential and Logarithmic Functions

  • Author

    Texas Instruments

  • Level

    9-12

  • Activity Time

    45 Minutes

  • Device
    • TI-Nspire™ Apps for iPad®
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      TI-Nspire™ CX
    • ax-icon-color-device
      TI-Nspire™ CX CAS
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  • Software

    TI-Nspire™
    TI-Nspire™ CAS

  • TI-Nspire Version

    3.2

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Comparing Exponential and Power Functions

Published on 12/02/2011

Activity Overview

Students will be able to use various graphical representations to determine which of two functions is greater for large values of x.

Objectives

  • Students will be able to use various graphical representations to determine which of two functions is greater for large values of x.
  • Students will understand that any exponential function of base greater than 1 will be greater than any power function for sufficiently large values of x.
  • Students will be able to determine which of two functions is greater given a graph of the ratio of the two functions.
  • Students will be able to construct arguments based on graphs and other reasoning to support the conclusion that exponential functions exceed power functions for sufficiently large values of x.

 

Vocabulary

  • Exponential function
  • Power function
  • Base

 

About the Lesson

This lesson provides several different opportunities for students to explore graphical relationships between different exponential and power functions, including an investigation of the ratio of the two functions.