Skip to ContentGo to accessibility page
OpenStax Logo
Algebra 1

5.8.3 Using Function Language and Notation

Algebra 15.8.3 Using Function Language and Notation

5.8.3 Using Function Language and Notation

5.8.3 • Using Function Language and Notation

Activity

An exponential function is written in the form  f ( x ) = a b x f ( x ) = a b x , where a a is the initial value and b b is the growth factor.

1. In a biology lab, a population of 50 bacteria reproduce by splitting. Every hour, on the hour, each bacterium splits into two bacteria.

a. Write a sentence of the form “_____ is a function of _____.”

b. Indicate which is the independent and which is the dependent variable.

c. Write an equation that represents the situation using function notation.

2. Every year after a new car is purchased, it loses 1 3 1 3 of its value. Let’s say that the new car costs $18,000.

a. Write a sentence of the form “_____ is a function of _____.”

b. Indicate which is the independent and which is the dependent variable.

c. Write an equation that represents the situation using function notation.

3. To control an algae bloom in a lake, scientists introduce some treatment products. The day they begin treatment, the area covered by algae is 240 square yards. Each day since the treatment began, a third of the previous day’s area (in square yards) remains covered by algae. Time t t is measured in days.

a. Write a sentence of the form “_____ is a function of _____.”

b. Indicate which is the independent and which is the dependent variable.

c. Write an equation that represents the situation using function notation.

Video: Writing an Exponential Function from a Situation

Watch the following video to learn more about exponential functions:

Writing an Exponential Function from a Situation

Self Check

A new computer is purchased for $2,500. Each year after its purchase, it loses 1 5 of its value. Which equation represents this situation?
  1. f ( t ) = 4 5 ⋅ ( 2500 ) t
  2. f ( t ) = 2500 ⋅ ( 4 5 ) t
  3. f ( t ) = 2500 ⋅ ( 4 5 ) t
  4. f ( t ) = 2500 + ( 4 5 ) t

Additional Resources

Writing Functions from Exponential Situations

EXPONENTIAL GROWTH

A function that models exponential growth grows by a rate proportional to the amount present. For any real number x x and any positive real numbers a a and b b  such that b ≠ 1 b ≠ 1 , an exponential growth function has the form

f ( x ) = a b x f ( x ) = a b x

where

  • a a is the initial or starting value of the function.
  • b b is the growth factor or growth multiplier per unit x x .

Example 1

The starting value of the function is 10.   This function doubles every year.

Example 2

An acre of land is worth $40,000 at the time of purchase. It doubles in value every decade. Write an equation for this situation where t t is time in decades.

Try it

Writing Functions from Exponential Situations

1. The starting value of the function is 150. This function triples every decade

2. When first measured, the population of deer in a forest is 40. Over time, the population triples every year. Write an exponential equation where t t  is time in years.

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.