Relating to a mathematical expression containing one or more exponents. ♦ Something is said to increase or decrease

**exponentially**if its rate of change must be expressed using exponents. A graph of such a rate would appear not as a straight line, but as a curve that continually becomes steeper or shallower.Similarly, you may ask, what is an exponential graph?

**Graphs**of

**Exponential**Functions. The

**graph**of y=2

^{x}is shown to the right. Here are some properties of the

**exponential**function when the base is greater than 1. The

**graph**passes through the point (0,1) The domain is all real numbers.

What does it mean to have an exponential relationship?

**Exponential relationships**are

**relationships**where one of the variables is an exponent. So instead of it being '2 multiplied by x', an

**exponential relationship**might have '2 raised to the power x': Usually the first thing people do to get a grasp on what

**exponential relationships**are like is draw a graph.

What does it mean when a graph is exponential?

Notice on the

**graph**that, as the value of x increases, the value of f(x) also increases. This**means**that the function is an increasing function. The inverse of an**exponential**function is a logarithmic function and the inverse of a logarithmic function is an**exponential**function.