# 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-Navigator™

TI Connect™

• ##### Accessories

TI Connectivity Cable

• ##### Other Materials
This is Activity 6 from the EXPLORATIONS Book:
Exploring Mathematics with the Transformation Graphing Application.

## Exploring the Exponential Function

#### Activity Overview

Students study the exponential function and differentiate between exponential growth or decay from an equation. They identify the coefficient in an equation that represents the rate of growth/decay. Students also explain the effect of changes in the values of A and B.

#### 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 73 - 83 from the attached PDF file for your class
• #### During the Activity

Distribute the pages to the class.

• Enter an exponential function ABx in the calculator and set the values of the coefficients to 1
• Observe the graph
• Change the value of A and observe the effects on the y-intercept
• Set A=1 and increase the value of B
• Observe that B controls the rate at which the function grows
• Explore how money deposited in a bank earning interest shows exponential growth
• Examine how the cooling curve, as a cup of hot chocolate cools, represents exponential decay
• Observe that the exponential equation is asymptotic to zero
• Study various graphs, determine whether they are growing or decaying, and find the values of A and B
• #### 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