07 - What is an Exponential Function? (Exponential Growth, Decay & Graphing).

In this lesson, you will learn about the exponential function and its applications in math, science, and engineering. The exponential function is very simply a base raised to an exponent. The value of the base determines the shape of the graph of the exponential curve.
Exponential growth occurs when the base is greater than one. Exponential decay occurs when the value of the base is between zero and one. The base isn't allowed to be less then zero in an exponential function.

In this lesson we will graph the exponential function and discuss the shape of the curve. We will learn when the graph represents exponential growth and when it implies decay. We will also discuss applications of the exponential function in all branches of science, math, and engineering.

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For the guys who do not understand why when 0 < b < 1 works in the way it does is just because when we have a fraction on the negative power we can always transform it to an integer with positive power. This is true for all exponents - x^-1 = 1/x and (1/x)^-1 = x^1. Example - 3 ^ -1 = 1/3^1 and (1/3)^-1 = 3^1

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