Activity Detail
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Modeling Exponential Decay with a Look at Asymptotes - Activity 7
 


Activity Overview

Students use sample data to approximate models with the Transformation Graphing Application. They are introduced to the idea of discrete data sets being used with continuous function models. They also identify non-zero asymptote form of an exponential function.

Before the Activity

Install the Transformation Graphing application on the students' graphing calculators using one of these two methods:
  • TI-Connect™,  a TI Connectivity Cable, and the Unit-to-Unit Link Cable
  • TI-Navigator™  "send to class" feature
  • See the attached PDF file for detailed instructions for this activity
  • Print pages 89 - 96 from the attached PDF file for your class

    		•

    		During the Activity

    		Distribute the pages to the class.
    Follow the Activity procedures:
  • Record the number of dice used for the trial
  • Roll the dice
  • Remove from the set any dice that shows a 6 on its top face
  • Record the number of remaining dice in the set
  • Use only the dice left, roll these dice, and remove any dice that shows a 6
  • Repeat until no dice remain, or the dice have been rolled 15 times, 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 and use the guess-and-check method to find a reasonable model for the data
  • Observe that the decaying curve does not reach zero, but tends to zero
  • Write an equation for 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 the activity with non-standard set of dice

    		After the Activity

    		Students will complete the Student Worksheet and answer questions.
  • Review student results
  • As a class, discuss questions that appeared to be more challenging
  • Re-teach concepts as necessary

    		Other Downloads




    view standards alignment
    view textbook alignment

    Subject Area:
    Math : Algebra I : Exponential Functions

    Author:
    Texas Instruments

    Level:
    9-12

    Activity Time:
    90 Minutes

    Device:
    TI-83 Plus Family, TI-84 Plus Family

    Apps:
    Transformation Graphing

    Software:
    TI Connect™

    Accessories:
    TI Connectivity Cable, Unit-to-Unit link cables

    Other:
    This is Activity 7 from the EXPLORATIONS Book:
    Exploring Mathematics with the Transformation Graphing Application.
    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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