Chapter 8.1, Problem 58PPS

To determine

To find the number of people attended the South High School football games in 2015.

Answer to Problem 58PPS

  $7464$

Explanation of Solution

Given:

Total attendance at games for both schools since 2010, $T=-0.69x^3+55.38x^2+643.31x+10,538$

Number of people at games for North High School since 2010, $N=-3.78x^3+58.96x^2+265.96x+5257$ .

Concept used:

Number of people at South High School football games, $S=T-N$ .

Calculation: Number of people at South High School football games is given by $S=T-N.$

  $\begin{array}{l}\Rightarrow S=\left(-0.69x^3+55.38x^2+643.31x+10,538\right)-\left(-3.78x^3+58.96x^2+265.96x+5257\right)\\ \Rightarrow S=-0.69x^3+55.38x^2+643.31x+10,538+3.78x^3-58.96x^2-265.96x-5257\end{array}$

  $\Rightarrow S=-0.69x^3+3.78x^3+55.38x^2-58.96x^2+643.31x-265.96x+10,538-5257$

  $\Rightarrow S=3.09x^3-3.58x^2+377.35x+5281$

Therefore, number of people at South High School football games is modeled by the equation

  $S=3.09x^3-3.58x^2+377.35x+5281$

Now,

Number of people attended the South High School football games in 2015 is given by

  $S=3.09x^3-3.58x^2+377.35x+5281$

Number of years, $x=2015-2010$

         $=5$

  $\Rightarrow S=3.09x^3-3.58x^2+377.35x+5281$

  $\begin{array}{l}\Rightarrow S=3.09\times {\left(5\right)}^3-3.58\times {\left(5\right)}^2+377.35\times \left(5\right)+5281\\ \Rightarrow S=3.09\times 125-3.58\times 25+377.35\times \left(5\right)+5281\\ \Rightarrow S=386.25-89.5+1886.75+5281\\ \Rightarrow S=386.25+1886.75+5281-89.5\\ \Rightarrow S=7554-89.5\\ \Rightarrow S\approx 7464\end{array}$

Conclusion:

Therefore, number of people attended the South High School football games in 2015 is $7464$ .