Course: College Algebra
Topic: Exponential and Logarithmic Functions
Subtopic: Applications


In this lesson we apply the skill of solving exponential and logarithmic equations by translating growth and decay application problems into such an equation and then solving. The growth and decay applications include problems such as viruses spreading exponentially, nuclear waste decaying exponentially, and logarithmic learning curves. These will be important processes in calculus where our primary focus will be on the rate of change of this growth or decay.


By the end of this topic you should know and be prepared to be tested on:


Terms you should be able to define: exponential growth, exponential decay, initial amount, growth constant "k", doubling time, carbon dating, compound interest, principle (in terms of money invested)

Text Notes

Be sure to practice a variety of applications exponential and logarithmic, growth and decay. You are expected to memorize the exponential growth model formula. You are not expected to memorize other application formulas (e.g. Newton's Law of Cooling, Logistic Growth Model), but you should know how to use them when applicable.

You may SKIP any "curve fitting" and "regression" examples/problems in this section and throughout the course.

Mini-Lectures and Examples

STUDY: Application of Exponential and Logarithmic Functions

Supplemental Recources (recommended)

Read article: What Exponential Growth Really Looks Like which includes how exponential growth can be misrepresented to make things look like they have strong growth when they don't. Deception in graphs used in advertising and marketing materials is prolific and potentially dangerous.

Supplemental Resources (optional)

If you need supplemental tutorial videos with examples relevant to this section go to James Sousa's MathIsPower4U and search for topics below:
"Solving Applications Using Logarithmic Equations"
"Solving Applications of Exponential Growth and Decay"
"Solving Applications Using Exponential Equations" (SKIP regression vids)

rev. 2020-11-02