# Activities

• • • ##### Subject Area

• Math: Algebra I: Exponential Functions

• ##### Author 9-12

90 Minutes

• ##### Device
• TI-83 Plus Family
• TI-84 Plus
• TI-84 Plus Silver Edition

TI Connect™

• ##### Accessories

TI Connectivity Cable

• ##### Other Materials
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

## 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.

• 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