Modeling Exponential Decay with a Look at Asymptotes - Activity 7

Author

Texas Instruments

Alignment

Standards Alignment

Textbook Alignment

Subject Area

Math: Algebra I: Exponential Functions

Level

9-12

Activity Time

90 Minutes

Software

TI Connect™

TI Calculator

TI-83 Plus Family

TI-84 series

Applications

Transformation Graphing for TI-83 Plus and TI-84 Plus

Other Materials

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

Resource Types

Lessons

Report an Issue

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

Download Files

Download All Files (ZIP)

Before the Activity Files

Teacher Notes Appendix A PDF Teacher Notes Appendix B PDF Teacher Notes PDF

Author

Texas Instruments

Alignment

Standards Alignment

Textbook Alignment

Subject Area

Math: Algebra I: Exponential Functions

Level

9-12

Activity Time

90 Minutes

Software

TI Connect™

TI Calculator

TI-83 Plus Family

TI-84 series

Applications

Transformation Graphing for TI-83 Plus and TI-84 Plus

Other Materials

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

Resource Types

Lessons

Report an Issue

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Modeling Exponential Decay with a Look at Asymptotes - Activity 7

Transformation Graphing for TI-83 Plus and TI-84 Plus

Modeling Exponential Decay with a Look at Asymptotes - Activity 7

Before the Activity Files

Transformation Graphing for TI-83 Plus and TI-84 Plus

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