5.11.7 Lesson Summary

In this lesson, you learned how to:

• Use exponential functions to model situations that involve exponential growth or decay.
• Determine an appropriate model for a situation described by data.

Here are the activities that helped you reach those goals:

• 5.11.1: Changing the Graphing Window
  • In this activity, you thought about how changing the graphing window influences what you can see and understand about an exponential function
• 5.11.2: Choosing an Appropriate Model
  • In this activity, you examined the successive heights that a tennis ball reached after several bounces on a hard surface and considered how to model the relationship between the number of bounces and the height of the rebound. To do so, you determined the growth factor of successive bounce heights.
  • 5.11.2: Self Check
  • 5.11.2: Additional Resources
• 5.11.3: Modeling with Exponential Function
  • In this activity, you had an opportunity to gather and analyze data for bounce heights for multiple balls. You processed your data and decided on an appropriate factor to quantify the bounciness of each ball. You became more comfortable with the fact that the data are not exactly exponential and with choosing different ways for deciding on an appropriate exponential decay factor.
  • 5.11.3: Self Check
  • 5.11.3: Additional Resources
• 5.11.4: Examine Exponential Decay in Context
  • In this activity, you continued to examine exponential decay in the context of successive ball bounces. You used the given data to calculate a rebound factor and used it to write a function that models the relationship between number of bounces and bounce heights. You then used the function to answer questions about the ball and its bounces.
  • 5.11.4: Self Check
  • 5.11.4: Additional Resources
• 5.11.5: Using Relationship Models to Answer Questions
  • In this activity, you used data to determine from what height, approximately, you thought a ball was dropped and were able to explain your reasoning.

After these activities, you completed the following practice:

• 5.11.6: Practice