Module 4

 Exponential and Logarithmic Functions

Learning Objectives

 

In this module you will become familiar with exponential and logarithmic functions. You will learn how to quickly sketch and recognize their graphs and to solve equations in which they appear, and you will learn how to use them in various applied situations.

 

After completing this module you should be able to:

 

·  Recognize applied situations involving exponential functions and logarithms

·  Quickly sketch rough graphs of exponential, logarithmic, and related functions

·  State the definition of the number e as a limit and use it to write formulas for quantities having continuous growth (eg. “continuously compounded interest”)

·  Convert exponential expressions to logarithmic form and vice versa

·  Simplify expressions involving logarithms and recognize equivalent expressions

·  Use logarithms to solve equations involving exponentials and vice versa

·  Apply these skills in a wide variety of practical situations

 

 

Each section of the notes for this module addresses some of these in more detail.

Section-by-Section Learning Objectives

            Section 0

 Introduction to Exponential Functions

            Section 1

 Exponential Functions of a Real Variable

            Section 2

 The number e and “natural” exponential functions

            Section 3

 Logarithms and Logarithmic Functions

            Section 4

 Working with Logarithms

            Section 5

 Exponential and Logarithmic Equations

 

 

Go To: Introduction  Sec 4.0  Sec 4.1   Sec 4.2   Sec 4.3   Sec 4.4   Sec 4.5   Lab