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

Jul 7, 2017

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 ${0.5}^{x}$...