IMathAS-libretexts

The following polynomial represents the number of major hurricanes that struck the U.S.

\displaystyle {x}

decades after 1911-1920

\displaystyle {y}={0.16}{x}^{{3}}-{2.32}{x}^{{2}}+{9.33}{x}-{2.21}

What is the end behavior of the function?

as $\displaystyle {x}\to\infty$ , $\displaystyle {y}\to\infty$
as $\displaystyle {x}\to\infty$ , $\displaystyle {y}\to-\infty$

Interpret the above end behavior in the context of the situation.

The following polynomial represents the revenue of a phone company (in thousands of dollars) when

\displaystyle {x}

thousand phones are produced.

\displaystyle {y}={\left({45}-{0.0125}{x}\right)}{x}

What is the end behavior of the function?

as $\displaystyle {x}\to-\infty$ , $\displaystyle {y}\to-\infty$
as $\displaystyle {x}\to-\infty$ , $\displaystyle {y}\to\infty$

Interpret the above end behavior in the context of the situation.

As a researcher you wish to create a polynomial to model the number of active duty military personnel (in millions)

\displaystyle {x}

years after 1997. Your research tells you that the number of active duty military personnel was originally decreasing, then increasing, then decreasing, and will continue to decrease in the future. You want to keep the degree as small as possible to keep the model simple.

What is degree should you use?

What should the sign of the leading coefficient be?

positive
negative

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