# How do you identify equations as exponential growth, exponential decay, linear growth or linear decay y=2x?

Jun 9, 2018

$y = 2 x$ represents linear growth

#### Explanation:

$y = 2 x$ is a linear equation whereby $y$ grows by 2 units for each unit increase of $x$. Hence, $y = 2 x$ represents linear growth.

Similarly, $y = - 2 x$ represents an example of linear decay.

Concerning exponential growth/decay::

$y = {2}^{x}$ represents an example of exponential growth. - See below
graph{2^x [-10, 10, -5, 5]}

$y = {2}^{-} x$ represents an example of exponential decay.. - See below
graph{2^-x [-10, 10, -5, 5]}