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Exponential Functions and their Graphs - Concept

Teacher/Instructor Carl Horowitz
Carl Horowitz

University of Michigan
Runs his own tutoring company

Carl taught upper-level math in several schools and currently runs his own tutoring company. He bets that no one can beat his love for intensive outdoor activities!

There are certain functions, such as exponential functions, that have many applications to the real world and have useful inverse functions. Graphing exponential functions is used frequently, we often hear of situations that have exponential growth or exponential decay. The inverses of exponential functions are logarithmic functions. The graphs of exponential functions are used to analyze and interpret data.

Exponential or power function are a new type of function. What they are are a function where instead of having x in the base of the problem where you say like x squared, x cubed and things like that. What we actually have is our variable moves to the exponent, moves to the top, okay? So a exponential power function is anything of the form a to the x. And there is a restriction on a and that it has to be greater than zero and it can't be 1. Reason it can't be 1 is if you have 1 to any power, it's just always going to remain 1. So it doesn't really make sense to have our base be 1 anyway.
Some language that goes along with this, okay? We call a the base and we call x the exponent, okay? So exponential power functions. Anything that is of the form a to the x with a being a positive number not equal to 1.

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