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\begin{document}

\noindent
\vfil \noindent
\large
\hfil Math 120 C - Autumn 2009 \hfil \pp
\hfil Mid-Term Exam Number Two\hfil  \pp
\hfil November 19, 2009 \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}
{\large
\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 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 Show all work for full credit.  
\item You have 50 minutes to complete the exam. 
\end{itemize}
\vfil
.

\newp

\begin{enumerate}

\item Azami has 60 meters of fencing with which to build a rectangular
enclosure.  On one side, she will leave gap so she can move things
in and out of the enclosure.  The gap will be one-third the
length of that side.  For example, the enclosure might look like this:

\epsfig{file=enclosure01.eps, 
 width=5cm,
 angle=0 }


What dimensions should the enclosure have to maximize the area of the enclosure?

\newp

\item In 1980, the city of Kolamto had a population of 40,000.
Kolamto's population doubles every 30 years.

In 2000, the population of the city of Jubnit was half that of Kolamto.
In 2005, Jubnit's population was 75\% as large as the population of Kolamto.

Assuming that Jubnit's population is growing exponentially, when will
the population of Jubnit reach 200,000?  Give your answer in years after
1980.

\newp

\item Leon works with weights every afteroon at the IMA.  
He has found that the amount of weight he can lift
is a linear-to-linear rational function of the number
of calories he ate for lunch.  
If he eats nothing (0 calories), he can
lift 50 kg. 

If he eats 400 calories, he can lift 100 kg.

The more he eats for lunch, the more he can lift, but he is never able to
lift more than 200~kg.

If he eats 300 calories for lunch, how much will he be able to lift?

\newp

\item Let $f(x)=6x-1$ and $g(x)=2x+5$.

\begin{enumerate}

\item Compute the composition $f(g(x))$.

\vfil

\item Let $h(x)=g(f(x))$.  Find $h^{-1}(x)$.

\vfil \vfil

\item Let $j(x) = (f(x))^2$.  Find the fixed points of $j(x)$.

\vfil

\end{enumerate}



\end{enumerate}





\end{document}


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