3.1 Exponential Functions and their Graphs

Why hello again blog post. It hasn't been long enough.

Friends, faculty, family members and random internet travelers: today I am here to tell you about exponential functions and their graphs.

Exponential functions can be written in the form

 

y = a * b^(x+c) + d

or you may see

 

f(x)= e^x

e is a constant that is an irrational constant around 2.7183, while x is a variable.

So, let's look at some graphs

 

This is actually a giraffe. But it's a common mistake. If that's actually what you were searching for, here's a video you might like:
http://www.youtube.com/watch?v=VDhNutbXpFE

Majestic, aren't they?
But really when graphing an exponential function it's important to identify:

•Asymptotes
 Start from the asymptote being y=0. Then it is important to look at two variables; c and d. In the exponential equation stated above c and d are both capable of shifting the graph up and down the graph.

•Intercepts
The x and y intercepts are found the same way as in any function. Plug in 0 for the y value to find the x-intercept and plug in 0 for the x value to find the y-intercept.

•Whether the graph is increasing or decreasing
If x doesn't have a negative coeffecient then the graph will increase. If the graph looks something like y=a*b^(-x) then it will decrease. The graph will also decrease if  0<b<1. Assuming a is postive. If a is negative then will the graph will reflect over the x-axis, reversing everything I just said.

It's also important to note how much the graph has been stretched by the value of b. As b gets larger the graph will be horizontally compressed and the opposite as it gets smaller. And the how much the graph has been shifted needs to be taken into account.

Some very basic examples:

A practical use of exponential functions is in compound interest.

Compound interest can be expressed in the formula

                 

A=P(1+r/n)^(nt)

 

A is the balance of the account, P is principal, t is the number of years, r is an annual interest rate and n is the number of times per year that the account compounds.

 

 

The book lickers must be stopped.

Operations Research is the place to be next year.

Peter's spheres are no match for mine.

Go frustums

 

Andrew