Question

How do you determine if the equation `y = 1/2 (5)^x` represents exponential growth or decay?

Answer 1

This function represent growth. For details see explanation.

Explanation:

To see if an exponential function is increasing or decreasing you look at the base. In a function `f(x)=a*b^x` and the coefficient `a`:

• the function is increasing if: `a>0` and `b>1` or `a<0` and `b<1`

• the function is decreasing if `a<0` and `b>1` or `a>0` and `b<1`