# How do you determine if the equation f(x) = 2(.44)^x represents exponential growth or decay?

Nov 4, 2017

As $x$ increases by $1 , f \left(x\right)$ is multiplied by $0.44$
So it represents exponential decay function.

#### Explanation:

f(x) = 2(0.44)^x ;

A function of the form $f \left(x\right) = a {b}^{x}$ , where $a > 0 \mathmr{and} 0 < b < 1$ is

an exponential decay function. Here $a = 2 \mathmr{and} b = 0.44$ .

$f \left(1\right) = 0.88 , f \left(2\right) = 0.3872 , f \left(3\right) = 0.170368 , f \left(4\right) = 0.0749619$

As $x$ increases by $1 , f \left(x\right)$ is multiplied by $0.44$

So it represents exponential decay function. [Ans]