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\begin{document}

\noindent
\vfil \noindent
\large
\hfil Math 120 A - Spring 2006 \hfil \pp
\hfil Mid-Term Exam Number Two\hfil  \pp
\hfil May 18, 2006 \hfil \pp
\normalsize
\vfil
\medskip
\hfil Name: \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 questions. 
\item You may use a calculator during this
examination.  
Other electronic devices are not allowed, and should be
turned off for the duration of the exam.
\item If you use a trial-and-error or guess-and-check method,
or read a numerical solution from a graph on your calculator
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.
\item Show all work for full credit.  
\item You have 50 minutes to complete the exam. 
\end{itemize}
\vfil
.

\newp

\begin{enumerate}

\item The population on the island of Blim is  a linear-to-linear rational function of time.
The population is always increasing, but it never exceeds 10,000.
In 1980 ($t=0$), there were 4,000 people on the island.
In 1990 ($t=10$), there were 5,000 people on the island.

In what year will there be 7,000 people on the island?

\newp

\item Maria is bicycling on a circular track.

She starts at point A and rides in the direction shown in the figure at a constant 25 m/sec.

She passes the southernmost point of the track 8.1 seconds after leaving point A.

She passes the northernmost point of the track 34.2 second after leaving point A.

\epsfig{file=track01.eps, 
 width=6cm,
 angle=0 }
 
 
How far east or west of point A will she be 15 minutes after leaving point A?

\newp

\item An interplanetary probe has determined that the
temperature on the surface of a certain planet is a sinusoidal function of time.
When the probe landed on the planet, the temperature was rising and it reached
a maximum of 190 degrees Celsius 3.6 hours later.
The temperate then decreased until it reached a minimum of 80 degrees Celsius
when the probe had been on the planet for 7.9 hours.

How many hours during each period is the temperature below 100 degrees Celsius?




\newp

\item Let $f(x)$ be defined like this:
\[
f(x) = \left\{ \begin{array}{ll}
			-7-x & \mbox{if $x \le -2$} \\
			3x+1 & \mbox{if $x > -2$} 
		\end{array}
	\right. 
\]

\begin{enumerate}
\item Write the multipart rule for the function $g(x) = f(x) + 2|x-1|$.
\vfil \vfil
\item Find all solutions to the equation $g(x)=3.$.
\end{enumerate}


\end{enumerate}

\end{document}


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