# How do you determine if y=0.2(5)^-x is an exponential growth or decay?

Jan 17, 2017

This is exponential decay. Two ways to tell are discussed below...

#### Explanation:

First, the negative exponent is an indicator of decay. You could rewrite the expression (without a negative exponent) as

$y = \frac{0.2}{5} ^ x$

This helps you to see that as $x$ gets very large, the expression gets very small - clearly not a case of growth.

Alternatively, you could make a chart in which you test increasing values of $x$, starting at $x = 1$ (for example) and increasing slowly to $x = 5$. You would see the results - the expression would decrease in value rapidly.