Chapter 7.3, Problem 38E

To determine

To Find: The Model $M$ for the annual education expenditures per student. Estimate the annual education per student in $2009$

Answer to Problem 38E

  $14665$

Explanation of Solution

Given: The total amount $I$ (in millions of dollars) of school expenditures from prekindergarten to a college level and the enrollment $P$ (in millions) in Prekindergarten through college can be modeled by

  $\begin{array}{l}I=\frac{17,913t+709,569}{1+0.028t}\\ P=0.5906t+70.219\end{array}$

Where $t$ is the number of years since $2001$ .

Given:

  $\begin{array}{l}I=\frac{17,913t+709,569}{1+0.028t}\\ P=0.5906t+70.219\end{array}$

Finding $M(8)$ since $2009$ is eight years from $2001$

Then

  $\begin{array}{l}M(t)=\frac{I(t)}{P(t)}\\ M(t)=\frac{\frac{17,913t+709,569}{1+0.028t}}{0.5906t+70.219}\\ M(t)=\frac{17,913t+709,569}{1+0.028t(0.5906t+70.219)}\\ M(8)=\frac{17,913(8)+709,569}{1+0.028(8)(0.5906(8)+70.219)}\\ Solving\\ M(8)\approx 14665\end{array}$

Hence, the annual education expenditures per student in $2009$ is nearly $14665$