Skip to ContentGo to accessibility page
OpenStax Logo
Algebra 1

5.10.3 Explore Average Rates of Change in an Exponential Decay Context

Algebra 15.10.3 Explore Average Rates of Change in an Exponential Decay Context

5.10.3 Explore Average Rates of Change in an Exponential Decay Context

5.10.3 • Explore Average Rates of Change in an Exponential Decay Context

Activity

Here is a graph you saw in an earlier lesson. It represents the exponential function p p , which models the cost p ( t ) p ( t ) , in dollars, of producing 1 watt of solar energy from 1977 to 1988, where t t  is years since 1977.

1. Clare said, “In the first five years, between 1977 and 1982, the cost fell by about $12 per year. But in the second five years, between 1983 and 1988, the cost fell only by about $2 a year.” Show that Clare is correct.

2. If the trend continues, will the average decrease in price be more or less than $2 per year between 1987 and 1992? Be prepared to show your reasoning.

Are you ready for more?

Extending Your Thinking

Suppose the cost of producing 1 watt of solar energy had instead decreased by $12.20 each year between 1977 and 1982. Compute what the costs would be each year and plot them on a graph. Compare your graph to the graph from the beginning of the 5.10.3 activity (top of page). How do these alternate costs compare to the actual costs shown?

Self Check

The graph below shows the bounce height of a basketball at each bounce. What is the approximate average rate of change from the first bounce to the third bounce?

  1. -600
  2. 600
  3. -300
  4. 300

Additional Resources

Trends in Average Rates of Change

A construction company purchased some equipment costing $300,000. The equipment depreciates in value over time.

Approximately how much did the value drop from years 0 to 5 compared to years 6 to 10?

v ( 5 ) − v ( 0 ) 5 − 0 ≈ 140 , 000 − 300 , 000 5 = − 32 , 000 v ( 5 ) − v ( 0 ) 5 − 0 ≈ 140 , 000 − 300 , 000 5 = − 32 , 000

v ( 10 ) − v ( 6 ) 10 − 6 ≈ 70 , 000 − 120 , 000 4 = − 12 , 500 v ( 10 ) − v ( 6 ) 10 − 6 ≈ 70 , 000 − 120 , 000 4 = − 12 , 500

Following this trend, we would expect the average rate of change of the value of the equipment from years 11 – 15 to be below –12,500 dollars per year.

Try it

Trends in Average Rates of Change

Approximately how much did the value drop from year 11 to year 15?

PreviousNext
Order a print copy
Citation/Attribution
Reuse and redistribution of this content in digital or print format:
  • This book may not be used in the training of large language models or otherwise be ingested into large language models or generative AI offerings without OpenStax's prior written permission.
  • This book uses the Creative Commons Attribution-NonCommercial-ShareAlike License, which means that you can reuse and modify the material only for noncommercial purposes, must attribute OpenStax, and must distribute any derivative works under the same license.
  • Any commercial printing of this textbook, including using a local or custom printer, must be approved by OpenStax, and proper citation provided.
  • OpenStax-copyrighted images, activities, assessments, and similar components of this book are subject to the same licensing – CC-BY-NC-SA. They can be used for noncommercial purposes with attribution. Commercial use requires permission.
  • Permission requests: Anyone who intends to incorporate this content (including text, images, and other components) into large language models, use it in AI offerings, use it commercially (including in print), and/or has questions about another use case is welcome to complete our reuse request form.
Attribution information
  • If you are redistributing all or part of this book in a noncommercial print format, then you must include on every physical page the following attribution:

    Access for free at https://openstax.org/books/algebra-1/pages/about-this-course

  • If you are redistributing all or part of this book in a noncommercial digital format, then for every page that includes OpenStax content, you must license the derivative work under the same CC-BY-NC-SA license as the original, and include on every digital page view the following attribution:

    Access for free at https://openstax.org/books/algebra-1/pages/about-this-course

Citation information

The information below includes the information needed to generate citations in most major styles (APA, MLA, etc.); you must reformat and organize the information as needed to fit the requirements of the style. Use the information below to generate a citation. We recommend using a citation tool such as this one.

© Apr 23, 2026 OpenStax. Textbook content produced by OpenStax is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike License. The OpenStax name, OpenStax logo, OpenStax book covers, OpenStax CNX name, and OpenStax CNX logo, and Rice University name, and Rice University logo trademarks, or wordmarks are not subject to the Creative Commons license and may not be reproduced without the prior and express written consent of Rice University.