1. Check it out! 3.5.2: Comparing Exponential Functions
3.5.2: Comparing Exponential Functions

2. On which bounce will the rebound be less than 50 centimeters?
A hard rubber ball will rebound to 75% of its height each time it bounces.
If the ball is dropped from a height of 200 centimeters, what will the height of each bounce be after 11 bounces? Create a table and a graph of the ball’s bounce rebound height over several bounces.
On which bounce will the rebound be less than 50 centimeters?
Common Core Georgia Performance Standard: MCC9–12.F.IF.9
3.5.2: Comparing Exponential Functions

3. At 0 bounces, the ball is at the initial height of 200 centimeters.
If the ball is dropped from a height of 200 centimeters, what will the height of each bounce be after 11 bounces? Create a table and a graph of the ball’s bounce rebound height over several bounces.
Begin by creating a table with the number of bounces and the height of the ball after each ball.
At 0 bounces, the ball is at the initial height of 200 centimeters.
After each bounce, the height is 75% of the previous height.
To calculate the height of the ball after 1 bounce, find 75% of 200, or 200 • 0.75.
3.5.2: Comparing Exponential Functions

4. The height after the first bounce is 150 centimeters.
To calculate the height of the ball after 2 bounces, find 75% of the previous height, or 150 • 0.75.
The height after the second bounce is centimeters.
Continue this way until the table is completed for 11 bounces.
3.5.2: Comparing Exponential Functions

5. Number of bounces Height of bounce (cm)
200 1
150 2
112.5 3
84.375 4
63.281 5
47.46 6
35.6 7
26.7 8 20 9 15 10 11
3.5.2: Comparing Exponential Functions

6. Use the table to plot the coordinates on a coordinate plane.
Label the x-axis “Number of bounces” and the y-axis “Height of bounce (cm).”
Plot each coordinate.
Notice that this scenario is best represented by the exponential function f(x) = 200(1 – 0.25) x.
3.5.2: Comparing Exponential Functions

7. 3.5.2: Comparing Exponential Functions
Height of bounce (cm)
Number of bounces
3.5.2: Comparing Exponential Functions

8. On which bounce will the rebound be less than 50 centimeters?
We can see from both the table and the graph that the height of the fifth bounce will be less than 50 centimeters.
Connection to the Lesson
As in the warm-up, students will create exponential functions from context.
Students will use their knowledge of writing exponential functions to analyze properties of exponential functions in order to make comparisons.
3.5.2: Comparing Exponential Functions