Exponential function IS JUST another function in mathematics study. To date, most of the time we are dealing with so called power function e.g  f(x) = x2
where x is the base
the number 2 is the power (index)
However, in exponential function we are dealing  f(x) = 2x
where 2 is the base
the number x is the power (index)
 source: Wikipedia

The big difference is in that the variable is now the power, rather than the base.

 source: Wikipedia
The most commonly encountered exponential-function base is the transcendental number e , which is equal to approximately 2.71828. Thus, the above expression becomes:(see also natural logarithm)
f (x) = e x

 Value of  e