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{\LARGE{
\hfil Math 120 A, B Autumn 2012 \hfil \pp
\hfil Mid-Term Exam Number Two\hfil  \pp
\hfil November 15, 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
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{\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}
}
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\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 Bob and Maria are moving in the $xy$-plane.
They move along straight lines at constant speeds.
They start moving at the same time.
Maria starts from the origin and heads toward the point $(15,12)$, reaching it in 3 seconds.
Bob leaves the point $(8,0)$ and heads toward the point $(0,2)$, reaching it in 
4 seconds.

\begin{enumerate}
\item Give Maria's parametric equations of motion.

\vfil

\item Give Bob's parametric equations of motion.

\vfil 

\item How long have Bob and Maria been moving at the instant
when they are closest together?
\vfil

\end{enumerate}

\newp

\item The mass of Bob's pancreas is a linear-to-linear function of time.
Today, it is 60 grams.  Ten days from now, it will be 105 grams.
Also, 170 days from now, it will be 145 grams.

When will Bob's pancreas have a mass of 75 grams?  Give your answer in days from today. 

\newp

\item The city of Arg has a rat problem.
In the year 2000, the population of Arg was 8000 and it grows at the rate of 5.4$\%$ per year.
In 2005, there were half as many rats as people in Arg, but the number of rats triples every
12 years.  

When will there be twice as many rats as people in Arg?  Give your answer in years after 2000.

\newp

\item 

\begin{enumerate}

\item Let $f(x)=3x-1$.  Suppose the graph of a function $b(x)$ is the graph 
of $f(x)$ shifted 3 units to the right and 6 units up.  Give the rule for $b(x)$.
\vfil
\item Let $g(x)=x+\sqrt{x^2-4}, x\ge 2$.  Find $g^{-1}(x)$ and specify its domain.
\vfil \vfil
\item Let $f(x)=3x-1$. Find a function $h(x)$ such that 
the function $k(x)=f(h(x))$ has $x=5$ as a fixed point.
\vfil
\end{enumerate}



\end{enumerate}

\end{document}


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