A condominium complex charges $185 per month for the homeowners’ association fee. The rates can rise every year because of inflation but they promise not to raise the rates more than 10% each year. Keep in mind, though, that if they raise the rate by 10% the first year, the second year is now more expensive. If they raise the maximum again, they are increasing the original $185 plus the first year’s adjustment by 10%. Graph the situation for 10 years.
How much could the homeowners’ fee be in ten years? Use the function
In this concept, you will learn to distinguish between exponential growth and exponential decay.
Exponential Growth and Decay
Sometimes you will need to identify whether a function is an exponential function. If your function can be written in the form
Therefore the function
In some cases with exponential functions, as the value increased, the value increased, too. This was a direct relationship known as exponential growth. As the
In other cases, as the
Examples
Example 1
Earlier, you were given a problem about the rising condominium fees. You need to determine how much the homeowners’ fee will be in ten years using the function where
First, make a table of values for the function
. 
0  1  2  3  4  5  6  7  8 

185  203.50  223.85  246.24  270.86  297.94  327.74  360.51  396.56 
Next, graph the function.
Example 2
Does the following function represent an exponential function? Graph the function.
First, answer the question.
No, this function does not represent an exponential function because the
Next, graph the function.
Example 3
Graph the function
First, graph the function.
Next, answer the question.
From the graph, the function exponential decay.
representsExample 4
Graph the function
and tell whether it represents exponential growth or decay.First, graph the function.
Next, answer the question.
From the graph, the function
represents exponential growth.Example 5
Graph the function
First, graph the function.
Next, answer the question.
From the graph, the function
Review
Graph each function. Then say whether it represents economic growth or decay.

y=12x