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\begin{document}
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\vfil \noindent

{\LARGE{
\hfil Math 120 C - Autumn 2014 \hfil \pp
\hfil Midterm Exam Number Two\hfil  \pp
\hfil November 13, 2014 \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
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{\Huge
\begin{tabular}{||c|c|r||} \hline 
 1 & 15 &\hspace{10mm} \hfil\\ \hline 
 2 & 15 &       \\ \hline
 3 & 15 &      \\ \hline
4 & 15 &    \\ \hline
Total & 60 & \\ \hline 
\end{tabular}
}
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\vfil
\begin{itemize}
\item This exam consists of FOUR problems on FIVE pages, including this cover sheet.
\item Show all work for full credit. 
\item You may use a scientific calculator during this
exam.  Graphing calculators are not permitted.
Also, other electronic devices are not allowed, and should be
turned off and put away for the duration of the exam.
\item You do not need to simplify your answers.
\item If you use a trial-and-error or guess-and-check method
when a more rigorous method is available, you will not receive full credit.
\item If you write on the back of the page, please indicate that you have done so!
\item You may use one hand-written double-sided 8.5" by 11" page of notes.
\item You have 50 minutes to complete the exam.
\end{itemize}

\vfil
{\small --}

\newpage

\begin{enumerate}

\item {\bf[15 points]} You would like to build a rectangular fence which will be divided into six sections in a $3\times2$ configuration, as shown below.\\[.1 in]
The material for the outside fence costs \$20 per foot, and the material for the inner partitions costs \$5 per foot.\\[.1 in]
If you have \$7200 total to spend, what is the {\bf maximum possible area} of the fence?
\vskip -.5 in
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\newpage

\item Abbi is downloading her favorite TV show online, but it's taking a while. In fact, the percentage of the show that's been downloaded after $t$ minutes is a linear-to-linear rational function of $t$.

At first, of course, the download is $0\%$ complete.

After $30$ seconds, the download is $5\%$ complete.

After $2$ minutes, the download is $16\%$ complete.

\begin{enumerate}
\item {\bf[13 points]} How much of the show has been downloaded after 30 minutes?
\vskip 6.5 in
\item {\bf[2 points]} Will the download ever finish? Explain.
\end{enumerate}

\newpage

\item {\bf[5 points per part]} \begin{enumerate}
\item Let $f(x) = 4^{2x-3}$. Compute $f(f(2))$.
\vskip 2.3 in
\item Let $f(x) = 4^{2x-3}$. Write a formula for the inverse function, $f^{-1}(x)$.
\vskip 2.6 in
\item Let $f(x) = 4^{2x-3}$. Explain how to turn the graph of $y = 4^x$ into the graph of $f(x)$.\\[.05 in] {\small (Do scratch work here, then fill in the blanks below.)}

\vskip 1.8 in

Fill in the blanks:\\[.1 in]

\begin{itemize}
\item First, you \underline{\qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad}.\\[.3 in]
\item Then, you \underline{\qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad}.
\end{itemize}
\end{enumerate}

\newpage

\item {\bf[5 points per part]} \begin{enumerate}

\item The city of Doublin has a population that doubles every 25 years.\\[.03 in]
In the year 2000, its population was 6000.\\[.1 in]
Write a function $f(t)$ for the population of Doublin, $t$ years after 2000.

\vskip 2 in

\item The city of Tripli has a population that triples every 30 years.\\[.03 in]
In the year 2016, its population was 4000 less than Doublin's.\\[.1 in]
Write a function $g(t)$ for the population of Tripli, $t$ years after 2000.

\vskip 3 in

\item When will the population of Tripli be twice the population of Doublin? Round your answer to the nearest year.

\end{enumerate}

\end{enumerate}

\end{document}