Online College Courses for Credit

Exponential Growth and Decay

Exponential Growth and Decay

Author: Seth Marx

To develop an understanding of exponential growth and exponential decay: how to determine which is which, and how to figure out a problem involving growth and decay.

We go over the basics of exponential growth and decay and then a couple sample problems.

Co-author: Rachel Kaplan

See More

Try Our College Algebra Course. For FREE.

Sophia’s self-paced online courses are a great way to save time and money as you earn credits eligible for transfer to many different colleges and universities.*

Begin Free Trial
No credit card required

47 Sophia partners guarantee credit transfer.

299 Institutions have accepted or given pre-approval for credit transfer.

* The American Council on Education's College Credit Recommendation Service (ACE Credit®) has evaluated and recommended college credit for 33 of Sophia’s online courses. Many different colleges and universities consider ACE CREDIT recommendations in determining the applicability to their course and degree programs.


New Terms

Exponential Growth: a function or model which begins increasing at a very slow rate, then keeps growing faster and faster; functions in the form of y = P(1 + r)t

Exponential Decay: a function or model which begins decreasing at a very slow rate, then keeps declining faster and faster;  functions in the form of y = P(1 - r)t

y = P(1±r)t: the function that determines exponential growth and exponential decay; for exponential growth, use a "+", and for decay, use a "-"; P is the initial amount started with, r is the rate of growth/decay, and t is the period of time; also, remember that the t is also the x-value

Explanation of Growth and Decay

Exponential Growth Sample Problem

Exponential Decay Sample Problem