Chapter 7.3, Problem 37E

To determine

To Find: The Model $M$ for the amount healthcare expenditures per resident. Estimate the annual healthcare expenditures per resident in $2010$

Answer to Problem 37E

  $8443$

Explanation of Solution

Given: The total amount $I$ (in millions of dollars) of healthcare expenditures and the residential population $P$ (in millions) in the United States can be modeled by

  $\begin{array}{l}I=\frac{171,000t+1,361,000}{1+0.018t}\\ P=2.96t+278.649\end{array}$

Where $t$ is the number of years since $2000$

Given:

  $\begin{array}{l}I=\frac{171,000t+1,361,000}{1+0.018t}\\ P=2.96t+278.649\end{array}$

Finding $M(10)$ since $2010$ is ten years from $2000$

Then

  $\begin{array}{l}M(t)=\frac{I(t)}{P(t)}\\ M(t)=\frac{\frac{171,000t+1,361,000}{1+0.018t}}{2.96t+278.649}\\ M(t)=\frac{171,000t+1,361,000}{1+0.018t(2.96t+278.649)}\\ M(10)=\frac{171,000(10)+1,361,000}{1+0.018t(2.96(10)+278.649)}\\ Solving\\ M(10)\approx 8443\end{array}$

Hence, the annual healthcare expenditures per resident in $2010$ is nearly $8443$