In mathematics, the exponential function is the unique real function which maps zero to one and has a derivative everywhere equal to its value. The exponential of a variable is denoted or , with the two notations used interchangeably.

The exponential function arises whenever a quantity's value increases in exponential growth and decreases in exponential decay. We can see more differences between exponential growth and decay along with their formulas in the following table. In exponential growth, a quantity slowly increases in the beginning and then it increases rapidly.

The formula of the exponential function is given as follows: f (x) = ax where a > 0 and a ≠ 1 and x ∈ R The most common exponential function is f (x) = ex, where 'e' is "Euler's Number" and its value is "e = 2.718...." The exponential curve depends on the exponential function and it depends on the value of the x.

where a > 0 and a ≠ 1 and x ∈ R The most common exponential function is f (x) = ex, where 'e' is "Euler's Number" and its value is "e = 2.718...." The exponential curve depends on the exponential function and it depends on the value of the x. The exponential function is classified into two types based on the growth or decay of an exponential curve: