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

Overview

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.

Objectives

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

• 4.5.1 Use the formula A=Iekt to solve exponential growth and decay application problems
• 4.5.2 Understand the growth constant k and be able to solve for it exactly when solving an exponential growth/decay application problem
• 4.5.3 Solve growth and decay problems including doubling time and carbon dating
• 4.5.4 Use the formula A=P(1+r/n)nt to solve compound interest application problems
• 4.5.5 Recognize a curve or point-plot as being linear, exponential, or logarithmic.

Terminology

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.

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)