# How do you determine if the equation y = 2(1/4)^x represents exponential growth or decay?

Oct 7, 2017

#### Explanation:

Growth/decay equations are always in the form:

$y = a {\left(b\right)}^{x}$ where $a =$initial amount, $b =$growth/decay factor,

and $x =$time

If $b > 1$, then the amount will get larger so exponential growth

If $b < 1$, then the amount will get smaller so exponential decay

if $b = 1$, then the amount will stay the same so its neither growth or decay. It’s just a constant value.

In your case, $b = \frac{1}{4}$ and $\frac{1}{4} < 1$ so it is exponential decay.