# How do you determine if the equation f(x) = 7(1/4)^x represents exponential growth or decay?

Dec 16, 2017

Observe the direction as 'x' is increased.

#### Explanation:

A growth function will have increasing $f \left(x\right)$ values. A decay function will have decreasing ones. A simple substitution of two values should be enough.
$f \left(x\right) = 7 \times {\left(\frac{1}{4}\right)}^{x}$

For x = 0, $f \left(x\right) = 7$

For x = 1, $f \left(x\right) = \frac{7}{4}$

For x = 2, $f \left(x\right) = \frac{7}{16}$

Definitely a decaying trend!