Power Functions

In this section, you will learn how to identify a power function and use interval notation to express its long-run behavior. If you need a refresher on how to use interval notation, now is a good time to review.

Learning Objectives

In this section, you will:

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

Figure 1

Suppose a certain species of bird thrives on a small island. Its population over the last few years is shown in Table 1.

Year	$2009$	$2010$	$2011$	$2012$	$2013$
Bird Population	$800$	$897$	$992$	$1,083$	$1,169$

Table 1

The population can be estimated using the function $P(t)=-0.3 t^{3}+97 t+800$ , where $P(t)$ 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.

Source: Rice University, https://openstax.org/books/college-algebra/pages/5-2-power-functions-and-polynomial-functions
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