# How do you tell whether f(x)=-(6/5)^-x is an exponential growth or decay?

Jun 24, 2017

exponential decay

#### Explanation:

To figure out whether a function represents exponential growth or decay, we must put it in the form $f \left(x\right) = a \cdot {b}^{x}$.

$- x$ is equal to $- 1 \cdot x$, so the function becomes

$f \left(x\right) = - {\left(\frac{6}{5}\right)}^{- 1 \cdot x}$

Since we know that ${\left(\frac{a}{b}\right)}^{-} 1$ is equal to $\left(\frac{b}{a}\right)$, we can rewrite the function in the form that we want.

$f \left(x\right) = - {\left(\frac{5}{6}\right)}^{x}$
or $f \left(x\right) = - 1 {\left(\frac{5}{6}\right)}^{x}$

If $0 < b < 1$, then the function represents exponential decay.
If $b > 1$, then the function represents exponential growth.

In our case, $0 < \frac{5}{6} < 1$, so this is exponential decay.