This problem deals with the type of functions known as exponential functions, which are written in the form Exponential functions describe percentage changes from an initial value . The constant graphically specifies the vertical intercept, and is the growth factor or decay factor. We start with the two functions that have a vertical intercept at .
The functions and has an intial value of of From the graph we can see that it corresponds to functions and
We can see that one function increases and decreases. The one that increases must correspond to since it has a growth factor and the function corresponds to the one that decreases.
We have two graphs left, and and two function rules. We can see that the graphs are both growing but at different rates.
If we look at the growth factors, we see that only grows s by for each step along the -axis, while grows rapidly by an entire . Thus, we can make our final conclusions.