Education Technology

Modeling Exponential Decay with a Look at Asymptotes

Published on 06/09/2008

Activity Overview

In this activity, students approximate exponential decay models by defining parameters A and B in the exponential equation y = abx. They identify non-zero asymptote form of an exponential function.

Before the Activity

  • Set up the Transformation Graphing Application on the calculator using the TI Connect™ software
  • See the attached PDF file for detailed instructions for this activity
  • Print pages 54 - 61 the attached PDF file for the class
  • During the Activity

    Distribute the pages to the class.

    Follow the Activity procedures:

  • Roll around 36 dice and remove from the set any die that shows a 6 on its top face
  • Using only the dice left, repeat the step until no die remains or there have been 15 trials, whichever occurs first
  • Enter the number of rolls and number of dice left as lists
  • Plot the graph and select an appropriate value for A
  • Change the value of B to obtain a proper decay rate
  • Observe that the decaying curve does not reach zero, but tends to zero
  • Write the equation of the exponential function
  • Determine when y < 0.5, and when there are no dice left
  • Use the calculator to get a rough estimate of the location of the asymptote
  • Repeat experiment with non-standard set of dice
  • After the Activity

    Students' will complete the Student Worksheet and answer questions listed on it.

    Review student results:

  • As a class, discuss questions that appeared to be more challenging
  • Re-teach concepts as necessary