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: Exponential Functions and Graphs

Overview

Since much of the material in this lesson is review from an intermediate algebra course, our focus here will be to expand on the basic topics, bump-up the level of difficulty, and get exponential functions down really well. As you work through the material, try to do what you can algebraically as well as take advantage of technology where appropriate.

Objectives

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

• 4.1.1 Understand the basic exponential function f(x)=a^x and its graph including being able to produce its graph both manually and electronically
• 4.1.2 Evaluate f(x)=a^x for given values of a and x both manually and electronically
• 4.1.3 Know the features of the graph of f(x)=a^x including basic shape, domain, range, intercepts, and asymptotes
• 4.1.4 Understand the effects of b, c, and d in y=b*a^(x-c)+d on the graph of f(x)=a^x including reflections, stretches and shrinks, vertical and horizontal shifts (translations)
• 4.1.5 Understand the natural exponential constant "e" including some history of its origin and application in science
• 4.1.6 Understand the natural exponential function f(x)=e^x and its graph including being able to produce its graph both manually and electronically
• 4.1.7 Evaluate f(x)=e^x for given values of x both manually and electronically

Terminology

Terms you should be able to define: exponential function, natural exponential constant "e"

Mini-Lectures and Examples

Supplementary Resources

Watch Dr. Albert Bartlett's Arithmetic, Population and Energy video which examines the arithmetic of steady growth in a finite environment. These concepts are applied to populations and to fossil fuels such as petroleum and coal. Although first given over 40 years ago, this presentation is highly recommended.
Eight 10-minute video segments: 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8