# Activities

• • • ##### Subject Area

• Math: Algebra I: Exponential Functions

• ##### Author 9-12

60 Minutes

• ##### Device
• TI-73 Explorer™
• TI-83 Plus Family
• TI-84 Plus
• TI-84 Plus Silver Edition
• TI-Navigator™
• ##### Software

TI InterActive!™

• ##### Accessories

CBL™/CBL 2™
CBR™/CBR 2™
TI Connectivity Cable

• ##### Other Materials
This is Activity 7 from the EXPLORATIONS Book:
TI InterActive!™ Data Collection and Analysis

## On the Rebound

#### Activity Overview

In this activity, students collect motion data for a bouncing ball using a motion detector. They analyze the data and attempt to find the exponential relationship between the bounce number and maximum height that the bounce reaches.

#### Before the Activity

• Connect the computer to the CBL 2™ using the TI connectivity cable

• Connect CBR 2™ to the DIG/SONIC port of the CBL 2™ unit
• Open a new TI InterActive!™ document
• See the attached PDF file for detailed instructions for this activity
• Print pages 41 - 46 from the attached PDF file for your class
• #### During the Activity

Distribute the pages to the class.

• Hold the motion detector 1.5 to 2 meters above the floor
• Hold a ball 0.5 meter below the detector and drop it
• Collect distance versus time data and plot a graph
• Record initial drop height as bounce zero and find the maximum heights of each successive bounce
• Plot bounce number versus bounce height
• Observe the graph is exponential in form and can be modeled by the equation y = ab^x
• Find the value of a - the initial height
• Find the ratio of maximum height of each bounce in relation to the preceding bounce
• Record the ratios and find the average ratio which represents b
• Enter the values of a and b in the equation to find y
• Observe this equation y = ab^x is a relationship between bounce height and bounce number
• Use the exponential model to find the height of the ball at the 8th bounce and also the number of bounces the ball makes before it no longer reaches a maximum height of 5 centimeters
• #### After the Activity

Students complete the analysis and answer questions.

Review student results:

• As a class, discuss questions that appeared to be more challenging
• Re-teach concepts as necessary

• If you use TI-Navigator™, you can download the attached EDC file and use as a quiz to check understanding. If you are using the TI-73, you may need the attached PDF.