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\begin{document}
\noindent
\vfil \noindent

{\LARGE{
\hfil Math 120 - Autumn 2014 \hfil \pp
\hfil Final Exam\hfil  \pp
\hfil December 6, 2014 \hfil \pp
\hfil Answers \hfil \pp
}}
\begin{enumerate}

\item $\dsps \frac{4 \tan{6 ^{\circ}}}{\tan{7^{\circ}} - \tan{6^{\circ}}} = 23.77880078...$ minutes

\item $\dsps \sqrt{\frac{{300304}}{37}} = 90.0906450433...$ feet

\item (a) $\dsps g(t) = 70 \left( 2^{t/5} \right)$ \\
(b) $\dsps c(t) = 31.5818(1.1606)^t$ \\
(c) $223.806$ seconds

\item (a)
\[
A(t) = \left\{
     \begin{array}{lr}
       120t+8000 &  \text{if $0 \le t \le 5$} \\
       8495-15(t-12) &  \text{if $5 \le t \le 12$}
     \end{array}
   \right.
\]

(b) $t=4.5$ and $t=9$

\item (a) $0.875$ hours after starting \\
(b) $x=2 \cos( 0.1 \pi + 1.6 \pi t), y=2 \sin (0.1\pi+1.6\pi t)$ \\
(c) $1.58859156...$ km

\item $w=10$

\item (a) $\dsps f(t)=\frac{60t+300}{t+30}$ \\
(b) $\dsps f^{-1}(y) = \frac{300-30y}{y-60}$.

\item (a) $f(t) = 38+2 \sin \left(\frac{2\pi}{14}(t-13.5) \right)$ \\
(b) $12.8304301...$ hours

\end{enumerate}

\end{document}


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