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Basic Exponential Functions

Functions where the input variable is found in the exponent.

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Exponentially Exciting

Credit: Michael Kent
License: CC BY-NC 3.0

An Exponential Graph [Figure1]

Basic Exponential Functions

Exponential functions take the form ax where a is a constant. From negative infinity to 0 it slowly increases, until finally it passes 0 and starts rapdily increasing. The Y value of an exponential function at 0 is almost 1. With such a rapid increase, what could these functions be useful for? Exponential functions are used growth and decay models. A common example of these is population growth. An example of decay is depreciating value of a car. The older a car is, the less value it has, and this decrease in value is exponential.

Creative Applications

1. Why does population growth follow an exponential model?

2. The amount of water left in a lake is halfed each year. Write an exponential function for the amount of water that would be left after X years, if they started with B amount of water.

3. Can you think of anymore examples of when exponential functions would be used?

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  1. [1]^ Credit: Michael Kent; License: CC BY-NC 3.0

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