1.6 Exponential and Logarithm Functions

Summary

By the end of your studying, you should know:

• The difference between an exponential growth rate and growth factor.
• The definition of a general exponential, including its graph.
• The definition of a general logarithm, including its graph.
• Laws of exponents.
• Laws of logarithms.
• Definition of the number e.
• The functions that comprise the Elementary Functions of calculus.

On-screen applet instructions: There is a show-and-hide button for the natural log function. How are e^x and ln(x) related?

Examples The ground noise created by an airplane taking off at time t = 0 is measured in decibels, and is given by where t is measured in seconds. How long will it be before the level of noise drops to 2 decibels? Find the inverse of and find the domains of f and f–1. Find all solutions to the equation ln(x + 4) = 2ln(x) – ln(2). Applets Comparing Exponential Functions Videos See short videos of worked problems for this section. Quiz Take a quiz. Exercises See Exercises for 1.6 Exponential and Logarithm Functions (PDF). Work online to solve the exercises for this section, or for any other section of the textbook.

Resources on the Web Information on Newton Biographical data from St. Andrew's University's Web site Excerpt from W.W. Rouse Ball's "A Short Account of the History of Mathematics" Information on Leibniz Biographical data from St. Andrew's University's Web site Excerpt from W.W. Rouse Ball's "A Short Account of the History of Mathematics" Calculus Applications Project Intermath Exponentials and Logs Wolfram Research

Interesting Application World record times for the mile-- are they exponential?

1.5 Trigonometric Functions

Table of Contents

1.7 Case Study: Modeling with Elementary Functions

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Copyright © 2005 Donald L. Kreider, C. Dwight Lahr, Susan J. Diesel