5.5.5 Writing Equations to Represent Exponential Decay

Algebra 15.5.5 Writing Equations to Represent Exponential Decay

Search for key terms or text.

Cool Down

Acetaminophen is a common pain reliever and fever reducer. Here is a graph showing the amount of acetaminophen, in milligrams, in an adult’s body at different times after they take a normal dose.

A graph showing acetaminophen levels (mg) decreasing over 8 hours; starting at 1000 mg at 0 hours, dropping to 750 mg at 1 hour, 562.5 mg at 2 hours, and continuing downward.

1. Answer the following questions.

a. What is the vertical intercept?

Compare your answer:

1,000

b. What does it mean in this situation?

Compare your answer:

There are 1,000 mg of acetaminophen in the person’s body after taking the medicine (this is the dose size).

2. What fraction of the medicine remained after one hour?

Compare your answer:

$\frac{3}{4}$ of the medicine remained after 1 hour since $\frac{750}{1000} = \frac{3}{4}$ .

3. Write an equation that represents the amount of medicine, $a$ , after $t$ hours.

Compare your answer:

$a = 1, 000 (\frac{3}{4})^{t}$

Previous Next

Citation/Attribution

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 permission.

Want to cite, share, or modify this book? This book uses the Creative Commons Attribution-NonCommercial-ShareAlike License and you must attribute OpenStax.

Attribution information

If you are redistributing all or part of this book in a 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 digital format, then you must 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

Use the information below to generate a citation. We recommend using a citation tool such as this one.
- Authors: Lynn Marecek, MaryAnne Anthony-Smith, Andrea Honeycutt Mathis, Jay Abramson, Sharon North, Amy Baldwin, Alyssa Howell
- Publisher/website: OpenStax
- Book title: Algebra 1
- Publication date: Jun 4, 2025
- Location: Houston, Texas
- Book URL: https://openstax.org/books/algebra-1/pages/about-this-course
- Section URL: https://openstax.org/books/algebra-1/pages/5-5-5-writing-equations-to-represent-exponential-decay

© May 21, 2025 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 are not subject to the Creative Commons license and may not be reproduced without the prior and express written consent of Rice University.