Activity Detail
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Modeling Exponential Decay with a Look at Asymptotes
 


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

    		Other Downloads




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    Subject Area:
    Math : Algebra I : Exponential Functions

    Author:
    Texas Instruments

    Level:
    9-12

    Activity Time:
    90 Minutes

    Device:
    TI-83 Plus Family

    Apps:
    Transformation Graphing

    Software:
    TI Connect™

    Accessories:
    TI Connectivity Cable

    Other:
    This is Activity 6 from the EXPLORATIONS Book:
    A Hands-On Look at Algebra Functions: Activities for Transformation Graphing .

    The following materials are required for this activity:

  • Sets of 6-sided dice (numbered 1 - 6)
  • Alternate (non-standard) sets of dice


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