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\newcommand{\pp}{\par \noindent}
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\begin{document}

\noindent
\vfil \noindent
\large
\hfil Math 120 A - Spring 2009 \hfil \pp
\hfil Mid-Term Exam Number Two\hfil  \pp
\hfil May 21, 2009 \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}
{\large
\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 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 Show all work for full credit.  
\item You have 50 minutes to complete the exam. 
\end{itemize}
\vfil
.

\newp

\begin{enumerate}

\item The people of a certain country are working to improve the
literacy rate (i.e., the percentage of the population who can read)
among them.  Today, the literacy rate is 50\%.
Their goal is to increase the literacy rate to 75\% in ten years,
and after that continuing to increase the literacy rate
indefinitely, ultimately getting closer and closer to 100\%.  

Suppose that the literacy rate is a linear-to-linear rational function of time.

\begin{enumerate}

\item Find the function that gives the literacy rate in terms of $t$, years
after today.

\vfil
\vfil

\item Find the inverse of the function you found in part (a).

\end{enumerate}

\newp

\item J\"{u}rgen is running clockwise around a circular track.
From his starting point, it takes him 14 seconds to reach the westernmost point
of the track.  It takes him 80 seconds from his starting point to reach the northernmost 
point of the track.  He runs at 3 meters per second.

\begin{enumerate}

\item After running for 8 minutes, how far (in a straight line) is J\"{u}rgen 
from the easternmost
point of the track?

\vfil

\vfil 

\item At the same time that J\"{u}rgen starts, Beatrice starts running counterclockwise
from the easternmost point at 4 meters per second.  
How long has Beatrice been running when she passes
J\"{u}rgen 
for the first time?

\end{enumerate}

\newp

\item The water pressure in a city water system varies sinusoidally.
At 4 AM today, the pressure was at a maximum: 100 psi (pounds per square inch).
After 4 AM, the pressure dropped, reaching the minimum pressure of 60 psi
at 10:30 AM today.

For how much time today (from midnight to midnight) is the water pressure
below 70 psi?


\newp

\item Each of the wheels of a bicycle has a radius of 33 cm.
The front sprocket has a radius of 7 cm.  What radius should the rear sprocket have
to achieve a speed of 25 km per hour while pedaling at 95 rpm (revolutions
per minute)?

 \epsfig{file=bike01.eps, 
 width=11cm,
 angle=0 }




\end{enumerate}





\end{document}


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