# How do you determine whether each function represents exponential growth or decay y=(0.5)^x?

Dec 11, 2017

As shown below:

#### Explanation:

For this problem we can sketch the function, what will be able to determine weather its decaying or not:

$y = {0.5}^{x} \equiv {2}^{- x}$:
As $x \to \infty , y \to 0$
and $x \to - \infty , y \to \infty$

graph{0.5^x [-9.08, 10.92, -2.72, 7.28]}

In general:

$y = {\beta}^{x}$

If $\beta > 1$ the function undergoes exponential growth
if $\beta < 1$ the function undergoes exponential decay
if $\beta = 1$ it represents a straight line