Activity Overview
Students collect the height versus time data of a bouncing ball using the CBR 2™. They find the relationship between the bounce number and the bounce height. They also learn to graph scatter plots, calculate the maximum value of a parabola, analyze and find an exponential regression for the rebound height.

Before the Activity

Use TI Connect™ to download Vernier EasyData™ application
See the attached PDF file for detailed instructions for this activity
Print pages 117 - 126 from the attached PDF file for the class

During the Activity
Distribute the pages to the class.
Follow the Activity procedures:

Retrieve time and bounce height data from Activity 12: Bouncing Ball
Record the X and Y coordinates of peaks as lists
Mark the vertices and join the points
Use the calculator to identify if a linear equation or an exponential equation is a better fit
Notice both functions have coefficients close to one and their graphed functions are not distinctive when plotted
Zoom and notice the exponential function is a better fit to the data peaks
Find the equation for the exponential function in the form Y = ab^x
Divide every vertex's Y-value by the previous vertex's Y-value, calculate the average and find the rebound percent
Use it to calculate the height of each successive vertex of a bounce
Use bounce height ratio, rebound percent, and initial drop height to write the exponential equation
Compare this equation with the one generated by the calculator
Determine how high the ball will bounce on its next bounce

After the Activity

Students analyze the results and answer the case analysis questions on the student worksheet.
Review student results
Discuss exponential functions being repeated multiplications
As a class, discuss questions that appeared to be more challenging
Re-teach concepts as necessary