# How do you determine if the equation #y=(1/2)^x# represents exponential growth or decay?

##### 1 Answer

Jul 12, 2016

The function decays exponentially.

#### Explanation:

Intuitively, you can determine if a function is exponentially growing (heading toward infinity) or decaying (heading toward zero) by graphing it or simply evaluating it at a few increasing points.

Using your function as an example:

It is clear that as

graph{(1/2)^x [-2.625, 7.375, -0.64, 4.36]}

You can see that the function rapidly approaches zero as

The rule to work by is that for