Elementary Algebra
Introduction to Algebra Linear Equations and Inequalities Functions and Graphs I Lines and thier Graphs Linear Systems Exponents & Polynomials
Intermediate Algebra
Factoring Rational Expressions Rational Equations and Applications Radical Expressions Nonlinear Equations and Applications Functions and Graphs II Exponential and Logarithmic Functions
Precalculus I / College Algebra
Equations and Inequalitites Functions and Graphs Polynomial and Rational Functions Exponential and Logarithmic Functions Systems and Matrices Geometry Basics Conic Sections Sequences and Series
Precalculus II / Trigonometry
The Six Trigonometric Functions Right Triangle Trigonometry Circular Functions Graphs of Trigonometric Functions Trigonometric Identities Trigonometric Equations Oblique Triangles and the Laws Vectors Complex, Parametric, and Polar Forms
Calculus I
Limits and Continuity Derivatives Analysis of Curves Antiderivatives
Calculus II
Transcendental Functions
Geometry Physics Integration Techniques Calculus of Infinity Parametric, Polar, and Conic Curves
Calculus III

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=Ie^(kt) to solve exponential growth and decay application problems (I is sometimes replaced by "A sub naught", A(t)=A_oe^(kt), but either way they mean the initial amount.)
• 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

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

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