# Exponential Functions

**Exponential Functions**

An exponential function is mathematically expressed as

f(y)=b^{y},

where “y” stands for the variable and “b” denotes the constant which is also termed as the base of the function.

The exponential function is mainly employed to determine exponential decay/ exponential growth. The most commonly used exponential function base is e.

**Exponential Function Rules**

Some important exponential rules are given below:

If a>0, and b>0, the following hold true for all the real numbers x and y:

- a
^{x}a^{y}= a^{x+y} - a
^{x}/a^{y}= a^{x-y} - (a
^{x})^{y}= a^{xy} - a
^{x}b^{x}=(ab)^{x} - (a/b)
^{x}= a^{x}/b^{x} - a
^{0}=1 - a
^{-x}= 1/ a^{x}