Skip to ContentGo to accessibility pageKeyboard shortcuts menu
OpenStax Logo
Algebra 1

5.13.3 Comparing Exponential Functions

Algebra 15.13.3 Comparing Exponential Functions
Search for key terms or text.

Activity

Here are graphs representing two functions and descriptions of two functions.

A graph with area (square inches) on the y-axis and time (months) on the x-axis; two upward-curving lines are shown, with a labeled point (p, q) where the lines intersect. The solid line has an y-intercept closer to 0 then the dashed line.
  • Function ff: The area of a wall that is covered by Mold A, in square inches, doubling every month.
  • Function gg: The area of a wall that is covered by Mold B, in square inches, tripling every month.

1. Which graph represents each function? Explain your answer.

2. When the mold was first spotted and measured, was there more of Mold A or Mold B? Explain how you know.

3. What does the point (p,q)(p,q) tell us in this situation? Explain your answer.

Self Check

In the formula f ( x ) = a ⋅ b x , what changes on the graph when a changes?
  1. The growth factor
  2. The slope
  3. The y -intercept
  4. The x -intercept

Additional Resources

Reading Exponential Graphs

The graphs of ff and gg are located below and are functions of the form y=a·bxy=a·bx.

Graph of exponential growth functions, f and g. Function g has a smaller y-intercept and climbs more quickly than function f.

Which curve has the larger aa value?

f(x)f(x) because its yy-intercept is higher.

Which curve has the larger bb value?

g(x)g(x) because it is growing more quickly.

Try it

Reading Exponential Graphs

The graphs of ff and gg are located below and are functions of the form y=abxy=abx.

Graph of exponential growth functions, f and g. Function f has a smaller y-intercept and climbs more quickly than function g.

Which curve has the larger bb value?

PreviousNext
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

© Jun 14, 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.