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{\LARGE{
\hfil Math 120 A - Spring 2013 \hfil \pp
\hfil Mid-Term Exam Number Two\hfil  \pp
\hfil May 23, 2013 \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}
}
\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 The older Magdalena gets, the taller she gets.
At the age of 5, she was 70 cm tall.
At the age of 30, she was 160 cm tall.
She will always get taller, and her height will approach, but never exceed 200 cm.

Suppose her height is a linear-to-linear rational function of time.

\begin{enumerate}
\item Find a function that gives her height as a function of time.

\vfil \vfil

\item At what age will Magdalena be 173 cm tall?


\end{enumerate}

\newp

\item Akira is running around a circular track.
Akira runs counterclockwise.
From where he starts, it takes him 18 seconds to reach the easternmost point of the track.
It takes him 80 seconds to run one complete lap.

\begin{enumerate} 
\item Let $r$ stand for the radius of the track.  With a coordinate system imposed
so that the origin is at the center of the track, express Akira's $x$- and $y$- coordinates
as functions of the time, $t$, since he started running (your expressions will involve $r$).

\vfil

\item Bob starts running at the same time as Akira.  
Bob starts from the westernmost point and runs clockwise.  
Bob and Akira pass each other for the first time after 30 seconds.
How long does Bob take to run one lap of the track?

\end{enumerate}

\newp

\item The population of city A increases by 1.9\% each year. In the year 2000, city A's population
was 10,000.

City B's population doubles every 18 years.  In the year 2005, there were twice as many people in 
city A as there were in city B.

When will the populations of the two cities be equal?  Give your answer in years after the year 2000.


\newp

\item 

\begin{enumerate}

\item Let $d(x)=5x-6$ and $r(x)=2x+4$.  Solve the equation $d(r(x))=1$.

\vfil

\item Let $k(x)=x^2-9x+21$.  Find the fixed points of $k(x)$.

\vfil

\item Let $f(x)=2x-7$.  Find a function $g(x)$ such that $f(g(x))=8x-3$.

\end{enumerate}

\end{enumerate}

\end{document}


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