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%\markboth{Dr. Matthew M. Conroy - University of Washington}{Dr. Matthew M. Conroy - University of Washington}

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\begin{document}
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{\LARGE{
\hfil Math 120 A - Autumn 2014 \hfil \pp
\hfil Mid-Term Exam Number Two\hfil  \pp
\hfil November 13, 2014 \hfil \pp
}}

\normalsize
\vfil
\medskip
\hfil Name: \hrulefill \hrulefill \hspace{0.25in} Student ID no. : \hrulefill

\vfil

\hfil Signature: \hrulefill \hrulefill \hrulefill \hrulefill \hrulefill \hspace{0.25in} Quiz Section (AA/AB/AC/AD): \rule{0.4in}{\linethickness} 
 
\vfil
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{\Huge
\begin{tabular}{||c|c|r||} \hline 
 1 & 10 &\hspace{10mm} \hfil\\ \hline 
 2 & 10 &       \\ \hline
 3 & 10 &      \\ \hline
4 &  10 &    \\ \hline
Total & 40 & \\ \hline 
\end{tabular}
}
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\vfil
\begin{itemize}
\item Complete all four questions. 
\item Show all work for full credit. 
\item You may use a scientific calculator during this
examination.  Graphing calculators are not allowed.
Also, other electronic devices are not allowed, and should be
turned off and put away for the duration of the exam.
\item If you use a trial-and-error or guess-and-check method
when an algebraic method is available, you will not receive full credit.
\item You may use one hand-written 8.5 by 11 inch page of notes.  Write
your name on your notesheet and turn it in with your exam.
\item You have 50 minutes to complete the exam. 
\end{itemize}
\vfil
%{\small{.$_{.}$}}
$.$

\newp

\begin{enumerate}

\item There were 10000 monkeys on Island X in 1930.
In 1945, there were 12000 monkeys on the island.
In 1935, there were half as many parrots as monkeys on the island.
The number of parrots doubles every 22 years.

Assuming the population of monkeys grows exponentially, when will there be three times as
many parrots as monkeys?  Give your answer in years after 1930.

\newp

\item You have 900 meters of fencing to build an enclosure next to a long building,
so fencing is not needed along the building side.
The enclosure will have a partition (made of the same fencing material) 
perpendicular to the building, as illustrated below.

\begin{tikzpicture}[scale=0.3]
\draw[line width=2pt] (0,0) -- (0,5) -- (14,5) -- (14,0);
\draw[line width=2pt] (10,5) -- (10,0);
\filldraw[fill=gray!20] (-8,0) rectangle (22,-5);
\draw (7,-2.5) node {building};
\end{tikzpicture}

\begin{enumerate}
\item 
What should the dimensions (length and width) of the enclosure be to maximize the area of the enclosure?

\vfil
\vfil
\vfil

\item What is the maximum possible area of the enclosure?

\end{enumerate}

\newp

\item The more you study for the Math 120 final exam, the better your score will be, but you cannot exceed
100 percent.  If you study for 4 hours, you will get a score of 45 percent.
If you study for 16 hours, you will get a score of 75 percent.

Assume that the score you get on the final exam is a linear-to-linear rational function of the number of hours that
you study.

How many hours do you need to study to get a score of 85 percent on the final exam?

\newp

\item 
\begin{enumerate}
\item Find the fixed points of the function $\dsps f(x)=\frac{1}{2}x+\sqrt{x}$.
\vfil \vfil 
\item Restrict the domain of $\dsps j(x)=3x^2-12x+7$ to $x\le 2$  and find the function's inverse.
\vfil \vfil \vfil
\item Below is the graph of $y=g(x)$.
Determine the $x$-intercepts of $h(x)=\frac{1}{2}g(2x+5)$ (that is, the values of $x$ such that
$h(x)=0$).
\hspace{-9cm} \epsfig{file=fig.eps, 
 width=8cm,
 angle=270 }


\end{enumerate}



\end{enumerate}

\end{document}


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