# How do you determine if the equation y=(1/4)^x represents exponential growth or decay?

Mar 17, 2017

I would say decay:

#### Explanation:

You can see that for, say, $x = 2 , 3 , 4. . .$ your function always gives you a number one divided by something that is increasing every time resulting in a total number that gets smaller every time!
$\frac{1}{4} ^ 2 , \frac{1}{4} ^ 3 , \frac{1}{4} ^ 4. . .$

So, basically, as $x$ increases $\frac{1}{4} ^ x$ decreases!

Graphically:

graph{(1/4)^x [-10, 10, -5, 5]}