What is the Exponential Growth?

Exponential Growth is a type of growth of any quantity over a specific period of time. The term exponential is derived from the word exponent which means power. Therefore exponential growth is defined as the rate change i.e. change with respect to time of any quantity which is proportional to itself.
For example Alpha decay, the growth of bacteria
Graph

$f(x)=e^x$ is a type of exponential function. The graph of which can be demonstrated as,