Exponential Functions

What is an exponential function?

An exponential function is a mathematical expression in which a variable represents the exponent of an expression.

What does an exponential function look like?

Here's a very simple exponential function:

That equation is read as "y equals 2 to the x power."

Exponent refresher:

Let's remember how exponents work. Suppose we have the equation below:

That equation tells us to multiply x by itself to get y. It's the equivalent of:

If we want to find y when x=3, we can pretty quickly find that y=3*3=9. But, this is actually what's known as a "power function". In fact, it's just a polynomial, and not an exponential function at all.

Take a closer look at x2 . This means x squared or x to the second power. What does it mean?

We have two parts here:

1) An exponent,which is the number 2.
2) A base, which is the variable x.

With exponential functions, the variable will actually be the exponent, with a constant as the base.

Exponential Functions

Here's what exponential functions look like:

The equation is y equals 2 raised to the x power. This sort of equation represents what we call "exponential growth" or "exponential decay." Other examples of exponential functions include:

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