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Algebra 1

5.11.3 Modeling with Exponential Functions

Algebra 15.11.3 Modeling with Exponential Functions

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Activity

Your teacher will give your group three different kinds of balls.

Your goal is to measure the rebound heights, model the relationship between the number of bounces and the heights, and compare the bounciness of the balls.

A close-up of various sports balls, including footballs, soccer balls, and a basketball, piled together. The central football has Pro Touch Touchdown printed on it.

1. Create a table similar to the one below and begin your investigation. Make sure to note which ball goes with which column.

nn, Number of Bounces aa, Height for Ball 1 (cm) bb, Height for Ball 2 (cm) cc, Height for Ball 3 (cm)
0      
1      
2      
3      
4      

2. Which one appears to be the bounciest? Which one appears to be the least bouncy? Be prepared to show your reasoning.

3. For each one, write an equation expressing the bounce height in terms of the bounce number nn.

4. Explain how the equations could tell us which one is the most bouncy.

5. If the bounciest one were dropped from a height of 300 cm, what equation would model its bounce height hh?

6. Graph, on the same coordinate plane, the equation for each ball that models the bounce height hh after nn bounces using the Desmos tool below.

7. Use the graph of the equation that models the bounce height hh after nn bounces for all 3 balls to predict the difference in the height of Ball 1 after 5 bounces.

8. Use the graph of the equation that models the bounce height hh after nn bounces for all 3 balls to predict the difference in the height of Ball 2 after 5 bounces.

9. Use the graph of the equation that models the bounce height hh after nn bounces for all 3 balls to predict the difference in the height of Ball 3 after 5 bounces.

Are you ready for more?

Extending Your Thinking

1. If Ball 1 were dropped from a point that is twice as high, would its bounciness be greater, less, or the same? Be prepared to show your reasoning.

2. Ball 4 is half as bouncy as the least bouncy ball. What equation would describe its height hh in terms of the number of bounces nn?

3. Ball 5 was dropped from a height of 150 centimeters. It bounced up very slightly once or twice and then began rolling. How would you describe its rebound factor? Be prepared to show your reasoning.

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