# How do you determine if the equation #y = 4^x# represents exponential growth or decay?

##### 1 Answer

Since

#### Explanation:

The term that the exponent is attached to (in this case,

Since

This can be turned into a rule:

For the general exponential function

- the function represents
**growth**if#b>1# - the function represents
**decay**if#0 < b < 1#

We could imagine a decay function, say,

Here, as the exponent increases, the function value will *decrease*. Think along the lines of

graph{4^x [-12.52, 15.96, -3.28, 10.96]}

The function grows rapidly.

Whereas, the graph of

graph{(1/4)^x [-12.52, 15.96, -3.28, 10.96]}