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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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### Image Attributions

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

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