### LEARNING OBJECTIVES

By the end of this lesson, you will be able to:

- Identify power functions.
- Identify end behavior of power functions.
- Identify polynomial functions.
- Identify the degree and leading coefficient of polynomial functions.

Suppose a certain species of bird thrives on a small island. Its population over the last few years is shown below.

Year |
2009 | 2010 | 2011 | 2012 | 2013 |

Bird Population |
800 | 897 | 992 | 1,083 | 1,169 |

The population can be estimated using the function [latex]P\left(t\right)=-0.3{t}^{3}+97t+800,\\[/latex] where [latex]P\left(t\right)\\[/latex] represents the bird population on the island *t* years after 2009. We can use this model to estimate the maximum bird population and when it will occur. We can also use this model to predict when the bird population will disappear from the island. In this section, we will examine functions that we can use to estimate and predict these types of changes.