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{\LARGE{
\hfil Math 120 A - Winter 2015 \hfil \pp
\hfil Midterm Exam Number Two\hfil  \pp
\hfil February 26, 2015 \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 
 
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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 
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}
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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]} Rebecca is training to become a competitive eater. The time it takes her to eat a lobster is a linear-to-linear rational function of how long she spends practicing.\\[.1 in]
Without any practice, she can eat a lobster in $8$ minutes.\\[.1 in]
If she practices for three weeks, she can finish it in $5$ minutes and $6$ seconds.\\[.1 in]
If she practices for fifteen weeks, she can finish it in $3$ minutes and $10$ seconds.\\[.1 in]
How long should she practice in order to finish it in $2$ minutes and $30$ seconds?

\newpage

\item

\begin{enumerate}
\item {\bf[8 points]} Let $f(x) = \log_2(x) + 6$.\\[.1 in]
Solve the equation $f(f(x)) = 9$.
\vskip 3.2 in
\item {\bf[7 points]} Let $f(x) = \log_2(x) + 6$, and let $g(x) = \ln(x)$.\\[.1 in]
Using scaling, shifting, and/or reflecting, explain how to transform the graph of $g(x)$ into the graph of $f(x)$.\\[.1 in]
Show your work below. You don't have to graph either function. (But you may, if it helps you visualize things.)\\[.1 in]
{\small (Hint: Use some logarithm properties to rewrite $f(x)$.)}

\vskip 2.7 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[15 points]} You have $18$ cm of wire that you will use to create two shapes: a sector with central angle $1.6$ radians, and a rectangle that's twice as wide as it is long.

What should the radius of the sector be to {\bf minimize} the combined area of the two shapes?
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\draw node at (0.5,0.4) {\footnotesize $1.6$};
\draw [dashed,dash pattern = on 3 pt off 1 pt] (.3,0) arc (0:100:0.3);

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\newpage

\item \begin{enumerate}

\item {\bf[4 points]} The town of Beeattle has a {\bf bee} problem.\\[.1 in]
In the year $2000$, there were $5000$ bees. Each year, the number of bees grows by $2.5\%$.\\[.03 in]
Write a function $f(t)$ for the number of bees $t$ years after the year $2000$.

\vskip 1.4 in

\item {\bf[6 points]} The town of Beeattle also has a {\bf beetle} problem.\\[.1 in]
In the year $2010$, there were 200 bees per beetle.\\[.03 in]
The beetle population doubles every 40 years.\\[.03 in]
Write a function $g(t)$ for the number of beetles $t$ years after the year $2000$.

\vskip 2.8 in

\item {\bf[5 points]} The town of Beeattle also has a {\bf math} problem.\\[.1 in]
When will there be 300 bees per beetle? Round your answer to the nearest year.

\end{enumerate}

\end{enumerate}

\end{document}