Copyright © 2014, 2010, 2007 Pearson Education, Inc. Chapter 4 Exponential and Logarithmic Functions 4.1 Exponential Functions Copyright © 2014, 2010, 2007 Pearson Education, Inc. 1

Objectives: Evaluate exponential functions. Graph exponential functions. Evaluate functions with base e. Use compound interest formulas.

Definition of the Exponential Function The exponential function f with base b is defined by or where b is a positive constant other than 1 (b > 0 and b 1) and x is any real number.

Example: Graphing an Exponential Function We set up a table of coordinates, then plot these points, connecting them with a smooth, continuous curve. x –2 –1 1

Graphing form of an Exponential Function  

b determines whether you have a growth or decay: - if b > 1, growth - if 0 < b < 1, decay

Example: Transformations Involving Exponential Functions Use the graph of to obtain the graph of

Graph an Exponential!  

The Natural Base e  

Formulas for Compound Interest After t years, the balance, A, in an account with principal P and annual interest rate r (in decimal form) is given by the following formulas: 1. For n compounding periods per year: 2. For continuous compounding:

Example: Using Compound Interest Formulas A sum of $10,000 is invested at an annual rate of 8%. Find the balance in the account after 5 years subject to (a) quarterly compounding then (b) continuously compounding.