# How do you determine if the equation y=(0.5)^x represents exponential growth or decay?

May 12, 2016

I would say decay.

#### Explanation:

The way I would use is to write it as a fraction:
$y = {\left(\frac{1}{2}\right)}^{x}$
so, every time you increase $x$ the denominator becomes bigger and bigger and the numerator remains one; as a consequence, one divided by something becoming bigger and bigger gives you a number that becomes smaller and smaller!

Graphically you can see it as:
graph{(0.5)^x [-10, 10, -5, 5]}

Hope it helps!