# Activities

• • • ##### Subject Area

• Math: Algebra I: Exponential Functions

• ##### Author 9-12

90 Minutes

• ##### Device
• TI-83 Plus Family

TI Connect™

• ##### Accessories

TI Connectivity Cable

• ##### Other Materials
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

## 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.

• 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