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

Mar 26, 2018

When $x > 1$ it represents growth, when $x < 1$ it represents decay.

(When $x = 1$ it is a constant)

Mar 26, 2018

Check the sign of the exponent, and you will find that it represents exponential growth.

#### Explanation:

As $x$ increases in value, $y$ increases as well, and will approach infinity with increasing $x$. This is because the equation is raising 2 to $+ x$, indicating exponential growth (see below).

graph{2^x [-23.17, 56.83, -6.88, 33.12]}

If the equation was $y = {2}^{- x}$ y would be in exponential decay, with $y$ approaching 0 as $x$ goes to infinity. Again, we can show this on a plot (see below).

graph{2^(-x) [-23.17, 56.83, -6.88, 33.12]}

Basically, the sign of the exponent tells you if the function is increasing or decreasing.