# How do you determine if the equation y = 2.1(0.15)^x represents exponential growth or decay?

Apr 24, 2016

y decays as x increases..

#### Explanation:

Let $y = b {a}^{x} = b {e}^{x \ln a}$

$y ' = b \ln a {e}^{x \ln a}$

As x increases,,y is decreasing or increasing according as y' > or < 0.

For decay, y' < 0, when b > 0 and 0 < ln a < 1.#

Here, $b = 2.1 > 0 \mathmr{and} \ln a = \ln 0.15 = - 0.1897 < 0$

So, y decays as x increases.