3.1 Exponential Functions

 

 

 

3.1 Exponential Functions
The exponential function f with base a is denoted using

                
                      

  where , , and x is any real number

* a = 1 excluded because it yields f(x)=1 which is a constant

The graph of  is: 

Transformation of Graphs of Exponential Functions

Adding or subtracting from f(x) - the y value - shifts the graph of an exponential function up or down respectively:

     Examples:

• Adding two to shifts the graph up two units

                      

• The opposite is also true when subtracting two from f(x)= in that it will shift the graph down two units
•  

Conversely, adding or subtracting from the x value of the function shifts the graph left and right irrespectively

 

• Adding two to the x value of will shift the graph left two units 

• The opposite is also true when subtracting two from the x value of in that it shifts the graph right two units 

                           

  can also be reflected across the x and y axes when f(x)>0 and when x<0 respectively

                                                             

 

 

 NOTE - Be sure to examine when the y-intercept changes - or doesn't change - during each transformation

 

Compound Interest

Continuously Compounded Interest

P = Principal

R = Annual Interest Rate

N = Time

 

To account for more frequent (quarterly, monthly, daily) compounding of interest

 

n = Number of compounding's per year

t = Number of years

nt = total number of compoundings

 

Interest rate per compounding period is r/n, and the account balance after t years is:
 

 

                                                   

 

Examples of things that experience exponential growth or exponential decay are:

1. Population
2. Radioactivity
3. Interest