# What is an exponential function?

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An exponential function is a function of the form

For integer and rational

For irrational

Examples:

The last example illustrates why we also consider

We can write

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The exponential function is used to model a relationship in which a constant change in the independent variable gives the same proportional change in the dependent variable.

The function is often written as **exp(x)** It is widely used in physics, chemistry, engineering, mathematical biology, economics and mathematics.

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