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\noindent
\vfil \noindent
\large
\hfil Math 120 C - Autumn 2010 \hfil \pp
\hfil Mid-Term Exam Number Two\hfil  \pp
\hfil November 18, 2010 \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 & 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.  Graphic 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 Alex and Boris are moving in the $xy$-plane, along straight lines at constant
speeds.  
Alex starts at the origin and will reach the point $(9,6)$
after 3 seconds.  
Boris starts at the same time as Alex does.  
He starts from the point $(4,0)$ and will reach the point $(0,10)$ after 4 seconds.

When will Alex and Boris be closest together?

\newp

\item The population of city P triples every 35 years.
In the year 1995, city P's population was 60,000.

City Q's population has a constant doubling time. 
In 2005, the population of city Q was 10\% less than city P's population.  
In 2010, the population of city Q was 10\% more than city P's population.

 When will city Q's population reach 250,000? Give your answer in years after 1995.

\newp

\item The population of tigers in a certain region is always growing, but
will never surpass 1200.  In 1980, there were 300 tigers.  In 1985, there were 320 tigers.

Assume that the population of tigers is a linear-to-linear rational function of time.

When will there be 350 tigers?  Give your answer in years after 1980.
  
\newp

\item Let $f(x)=2x-3$ and $g(x)=x^2-6x$.

\begin{enumerate}

\item Let $m(x)=g(f(x))-f(g(x))$.  Find the vertex of the graph of $m(x)$.

\vfil

\item Let $(h,k)$ be the vertex you found in part (a).  Let $p(x)$ be
$m(x)$ restricted to $x\le h$.  Find $p^{-1}(x)$.

\end{enumerate}
  
\end{enumerate}
  
\end{document}


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