# How do you determine if the equation y=0.5(1.2)^x  represents exponential growth or decay?

Nov 21, 2017

See explanation.

#### Explanation:

An exponential equation $f \left(x\right) = a \cdot {b}^{x}$ is a decreasing function (represents decay) if:

$a > 0$ and bin(0;1)

or

$a < 0$ and $b > 1$

It is an increasing function (represents growth) if

$a < 0$ and b in (0;1)

or

$a > 0$ and $b > 1$

In the given example $a = 0.5$ (so $a > 0$) and $b = 1.2$ (so $b > 1$).

If we look at the above explanation we can say that $f \left(x\right)$ is an increasing function (represents growth)