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\begin{document}


\noindent
\vfil \noindent

{\LARGE{
\hfil Math 120 A Autumn 2011 \hfil \pp
\hfil Mid-Term Exam Number Two\hfil  \pp
\hfil November 17, 2011 \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}
}
\end{center}
\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 Bianca and Dennis are moving in the $xy$-plane at constant speeds along straight lines.
Biance starts from $(3,4)$ and reaches $(-8,2)$ in 8 seconds.
Dennis starts from $(-5,3)$ and heads toward $(1,0)$, getting there in 6 seconds.

\begin{enumerate}

\item Find Bianca's parametric equations of motion.

\vfil

\item Find Dennis' parametric equations of motion.

\vfil

\item When are Bianca and Dennis closest together?

\vfil

\end{enumerate}


\newp

\item Mortimer measures the length of the grass on his lawn at the same time every day.
The length of the grass on Mortimer's lawn is a linear-to-linear function of time.
Today, it is 3 cm high.  Tomorrow it will be 4 cm high.  One week from today, it will be 6 cm high.

\begin{enumerate}
\item How high will the grass be 30 days from today?

\vfil \vfil \vfil

\item When will the grass be 5 cm high?

\end{enumerate}

\newp

\item City A's population doubles every 19 years.  City B's population triples every 28 years.

In the year 2000, City A's population was 40,000.  

In 2010, City B's population was twice that of City A.

When will City B's population reach 500,000?  Express your answer in years after 2000.

\newp

\item Let $f(x)=x^2-10x+19$.

\begin{enumerate}

\item Let $g(x)$ be $f(x)$ restricted to $x \le 5$. Find $g^{-1}(x)$.

\vfil

\item Let $h(x)$ be the function whose graph is the result of shifting the graph of f(x)
3 units to the right and 4 units down.  Solve the equation
\[
h(x)=2.
\]


\end{enumerate}

\end{enumerate}


\end{document}


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