Objective: Students will find the
equation of an exponential
function using
data from an experimental situation.
Prior Knowledge: The student should be able to recognize exponential
data and graphs as well as enter
data into a graphing calculator.
Materials needed:
 a ball that bounces fairly well (tennis ball, golf ball, or super ball)
 Meter stick
 TI83 (or later) graphing calculator
Group size: 3 people
Time required: one 50minute class period
Procedure:
1. Tape a meter stick to a wall so that you can measure the
height of your ball at the top of successive bounces.
2. Hold the ball less than a meter above the ground, close to the meter stick and record the starting
height (at the bottom of the ball).
3. Drop the ball and record the
height of the bottom of the ball on the rebound of at least 5 bounces. Record your
data in a
table like the one below. Do at least 3 trials, starting from the same height. This is probably going to take several trials to get 3 that work!
Number of Bounces





0

(Start Height)

(Start Height)

(Start Height)

(Start Height)

1





2





3





4





5





4. Enter the Number of Bounces in List1 of your calculator and the Average
Height of the ball after each bounce in List2.
5. Test to see if this an exponential
equation by dividing each of your successive y values by the previous y value.
Do you get approximately the same ratio?
If so, what is it?
Does this
ratio show exponential growth or decay?
Does the
graph appear exponential?
How do you know?
What type of regression did you use?
y = ___________
Correlation (r value): ___
The ideal
equation to describe this situation is:
y = abx
a is the starting
height of the ball,
b is
percent of the previous
height the ball reaches on each bounce,
x is the number of bounces
8. How close is a to your start height?
9. How close is
b to the
ratio you found in #5?
10. Graph your regression (in Y1) on the
scatter plot of the data. How well does it fit the data?
Follow up questions:
1. If your first bounce is from a different height, does this
equation still work to predict the rebound heights of each bounce? Try dropping your ball from several different heights (change a in your equation) to support your answer.
2. Will this
equation work for another group’s ball? Try it and see.
3. Will this
equation work for a different type of ball? Why or why not?
4. Why did we use the average of each
height rather than every one of the individual measures?
5. Enter each of the individual measures into your calculator, and
graph your
equation through the points. How well does your
equation from #7 fit the data?
6. Use the calculator to find the exponential regression for all of the data. How close is it to the exponential regression you found in # 7? Which
equation fits all of the
data better?