# How do you determine if the equation y = 1/3 (0.1)^x represents exponential growth or decay?

May 3, 2017

See explanation.

#### Explanation:

An exponential function

## $f \left(x\right) = a \times {b}^{x}$

is:

• a decreasing function (represents decay) if $a > 0$ and b in (0;1) or $a < 0$ and $b > 1$

• an increasng function (represents growth) if $a < 0$ and $b > 1$ or $a < 0$ and b in (0;1)

For the given function:

$a = \frac{1}{3}$ and $b = 0.1$, so $a > 0$ and b in (0;1), therfore the function is decreasing (represents decay)