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{\LARGE{
\hfil Math 120 A, B Winter 2012 \hfil \pp
\hfil Mid-Term Exam Number Two\hfil  \pp
\hfil February 23, 2012 \hfil \pp
}}

\normalsize
\vfil
\medskip
\hfil Name: \hrulefill \hrulefill \hspace{0.5in} Student ID no. : \hrulefill

\vfil

\hfil Signature: \hrulefill \hrulefill \hrulefill \hspace{0.5in} Section: \hrulefill 
 
\vfil
\begin{center}
{\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}
}
\end{center}
\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
.

\newp

\begin{enumerate}

\item On a certain island, there are two species of birds, A and B.
The A population increases at the constant rate of 10$\%$ every 6 years.
The B population doubles every 7 years.

In the year 1990, the B population was 250, and the A population was 4000.

When will the populations be equal?  Give you answer in years after 1990.

\newp

\item You have 200 cm of wire with which to make two identical squares and a circle.
For example, you squares and circle might look like this:

\epsfig{file=wireProblem.ps, width=11cm, angle=0 }

\begin{enumerate}
\item What should the side length of the square be to {\textit{minimize}} the combined area
of the circle and the two squares?

\vfil

\item What should the side length of the square be to {\textit{maximize}} the combined area
of the circle and the two squares?

\end{enumerate}


\newp


\item A trough has a trapezoidal cross-section.
The trough is 10 feet deep.
The bottom of the trapezoid is 4 feet wide, and the top of the
trough is 9 feet wide.

\epsfig{file=trough.ps, width=11cm, angle=0 }

Water starts flowing into the trough.
The depth of the water in the trough 
increases at a constant rate of 0.3 feet per hour.

\begin{enumerate}

\item Give a function $w=f(t)$ relating the width $w$ of the surface of the water
to the time $t$ since water started flowing.

\vfil \vfil

\item Specify the domain of the function you gave in part (a).

\vfil

\item Give a function $t=f^{-1}(w)$ relating the time to the width of the surface of the water.

\vfil

\end{enumerate}

\newp

\item Consider the figure below illustrating a region bounded by two circular arcs.
The area of the striped region is 3920 square meters,
$z=40$ meters, and $s=126$ meters.  Find the value of $r$.

The figure is not to scale.

\epsfig{file=drawing1.ps,  width=7cm,  angle=0 }


\end{enumerate}

\end{document}


% \epsfig{file=pizza01.eps, 
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