Question

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

Answer 1

I would say decay.

Explanation:

The way I would use is to write it as a fraction:
`y=(1/2)^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!