Question

How do you determine if the equation `y = 0.5(4)^x` represents exponential growth or decay?

Answer 1

I would say an exponential growth.

Explanation:

You can obviously plot it but if you can also conside that in your function you have `4^x`; this tells you that as `x` increases (gets bigger) certainly `4^x` will increase as well (you can consider `4^2=16` and `4^3=64`). It is true that you have to multiply by `0.5` but nevertheless the entire function will grow anyway!

Graphically:
graph{0.5*(4^x) [-14.24, 14.24, -7.12, 7.12]}

If you want, try to think at the case where instead of having `4^x` you had `0.5^x`...