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# Basic Exponential Functions

## Functions where the input variable is found in the exponent.

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Exponential Functions

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Exponential functions are functions in the form \begin{align*}f(x)=a \cdot b^x\end{align*}  where the terms "a" and "b" are constants.  The constant "a" adjusts the value of the function when x=0, while the constant "b" adjusts the rate at which the the function increases (e.g. if b=2, the function would continuously double).  An example of an exponential function can be seen below.

Exponential functions are one of the most applicable to nature.  When there are no limiting factors, the population of mammals can be described as an exponential function.  Carbon-14, an isotope of Carbon that can be used to date artifacts, and other radioactive elements also have a property called half-life, which can be described with an exponential function.

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