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\vfil \noindent

{\LARGE{
\hfil Math 120 A - Winter 2016 \hfil \pp
\hfil Midterm Exam Number Two\hfil  \pp
\hfil February 25th, 2016 \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 & 15 &\hspace{10mm} \hfil\\ \hline 
 2 & 8 &       \\ \hline
 3 & 7 &       \\ \hline
 4 & 15 &      \\ \hline
5 & 15 &    \\ \hline
Total & 60 & \\ \hline 
\end{tabular}
}
\end{center}
\vfil
\begin{itemize}
\item This exam consists of FIVE 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 $^\circ$}

\newpage

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\node [black!70] at (5,6) {\huge HAPPY};
\node [black!70] at (5,4) {\huge BIRTHDAY};
\node [black!70] at (5,2) {\huge HAROLD!};
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\vspace{-1.6 in}

\begin{enumerate}

\item I'm starting a business selling slices of cake!\\[.1 in]
The number of slices of cake I'll sell each day is a {\bf linear} function of its price.\\[.1 in]
If I charge \$1.20 for a slice, then I will sell 82 slices per day.\\[.1 in]
If I charge \$3.95 for a slice, then I'll only sell 27 slices per day.
\begin{enumerate}
\item {\bf [6 points]} Give a function $f(x)$ for the {\em number of slices} I'll sell per day if I charge $\$x$ per slice.
\vskip 2 in
\item {\bf [3 points]} Give a function $g(x)$ for the {\em total amount of money} I'll make each day if I charge $\$x$ per slice.
\vskip 2 in
\item {\bf [6 points]} How much should I charge to maximize the amount of money I make?
\end{enumerate}

\newpage

Due to budget constraints, the following questions are very short.

\item {\bf [8 points]} In the following figure, the area of the shaded region is 9 square units.\\[.1 in]$\theta$ is $0.4$ radians. Find $x$.
\vspace{-.4 in}
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\node at (40:1.2) {$\theta$};
\end{tikzpicture}
\end{flushright}

\vskip 2.6 in

\item {\bf [7 points]} Let $f(x) = x^2+3^x$. Suppose we take the graph of $y = f(x)$ and do three things:
\begin{itemize}
\item First, scale it horizontally by a factor of $\frac13$.
\item Then, shift it 4 units to the left.
\item Then, reflect it vertically over the $x$-axis.
\end{itemize}
Write a function $g(x)$ for this new transformed graph.

\newpage

\item $f(x)$ is a {\bf linear-to-linear rational function} such that the curve $y = f(x)$ passes through the points $(1,-9)$ and $(10,60)$ and has vertical asymptote $x=7$.
\begin{enumerate}
\item {\bf [9 points]} Write a formula for $f(x)$.
\vskip 5 in
\item {\bf [6 points]} Write a formula for its inverse function, $f^{-1}(x)$.
\end{enumerate}

\newpage

\item People are moving out of Beattle (mostly because it's filled with bees).\begin{enumerate}
\item {\bf [4 points]} The population was $500,\!000$ in 2010, and every year it decreases by $3.7\%$.\\[.1 in]
Write a function $f(t)$ for the population of Beattle, $t$ years after 2010.
\vskip 1.5 in
\item {\bf [6 points]} Meanwhile, the number of bees in Beattle is growing exponentially!\\[.1 in]
In the year 2014, there was one bee for every person in Beattle.\\[.1 in]
In the year 2025, there will be three bees for every person in Beattle.\\[.1 in]
Write a function $g(t)$ for the number of bees in Beattle, $t$ years after 2010.
\vskip 3.5 in
\item {\bf [5 points]} When will there be five million bees in Beattle? Round your answer to the nearest year.
\end{enumerate}

\end{enumerate}

\end{document}