The formula for an exponential function is $LaTeX: y=c\cdot a^x$ , where C is the initial value (also called the vertical or y intercept) and A is the growth or decay rate. Remember in our first week of class when we found the relative change? This relative change is our growth or decay rate which gets repeated over and over again (much like the slope in absolute change).

One of the major uses of exponential functions is in investments. Investments, however, can have multiple compounding periods. In other words, instead of the investments having the percent compounded once a year (or once a time period) they can be divided up into multiple time periods. We will be doing an activity in class to learn how these multiple compounding periods will affect the overall investment. The different kinds of investment compounding equations we will be looking at are: compounding annually, compounding multiple times a year and compounding continuously.

The following practice problems come from My Open Math

A population numbers 11,000 organisms initially and grows by 8.5% each year. Write an exponential model for the population.
A population is currently 6,000 and has been increasing by 1.2% each day. Write an exponential model for the population.
The fox population in a certain region has an annual growth rate of 9 percent per year. It is estimated that the population in the year 2010 was 23,900. Estimate the fox population in the year 2018.
The amount of area covered by blackberry bushes in a park has been growing by 12% each year. It is estimated that the area covered in 2009 was 4,500 square feet. Estimate the area that will be covered in 2020.
A vehicle purchased for $32,500 depreciates at a constant rate of 5% each year. Determine the approximate value of the vehicle 12 years after purchase.
A business purchases $125,000 of office furniture which depreciates at a constant rate of 12% each year. Find the residual value of the furniture 6 years after purchase.
If $6,000 is invested in a bank account at an interest rate of 9 per cent per year, find the amount in the bank after 5 years if interest is compounded annually, quarterly, monthly, and continuously.