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

To see if an exponential function is increasing or decreasing you look at the base. In a function $f \left(x\right) = a \cdot {b}^{x}$ 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 $b < 1$