\documentclass[12pt]{report} 

\usepackage{palatino}
\usepackage{epsfig}
\usepackage[margin=0.8in]{geometry}

\usepackage{amsmath}
\usepackage{tikz}


%\markboth{Dr. Matthew M. Conroy - University of Washington}{Dr. Matthew M. Conroy - University of Washington}


\pagestyle{empty} %%% this results in no pagenumbers (footer is empty}

\setlength{\parindent}{0in}
\setlength{\parskip}{0.05in}

\baselineskip=20pt

\newcommand{\dsps}{\displaystyle}
\newcommand{\pp}{\par \noindent}
\newcommand{\newp}{\vfil \eject}

\begin{document}
\noindent
\vfil \noindent

{\LARGE{
\hfil Math 120 A - Autumn 2013 \hfil \pp
\hfil Mid-Term Exam Number Two\hfil  \pp
\hfil November 14, 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
\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 The population of the city of A triples every 22 years.
In the year 2000, the population of A was 10,000.

The city of A has a rat infestation problem.  In the year 2003, there
were 4 rats per person.  In the year 2012, there were 7 rats per person.
Assume the number of rats in the city is an exponential function of time.

\begin{enumerate}
\item
When will there be 3 million rats in the city of A?  Give your answer in years after 2000.

\vfil \vfil

\item How long does it take the number of rats in the city of A to double?

\end{enumerate}
\newp

\item The concentration of caffeine in a cup of tea is a linear-to-linear function of time.
Initially (i.e., when the tea is placed into hot water), it is zero.  
After steeping for one minute, it is 30 mg/ml.
After steeping for four minutes, it is 80 mg/ml.

\begin{enumerate}
\item What will the concentration be after 11 minutes?
\vfil \vfil
\item How long does the tea need to steep until the concentration is 140 mg/ml?
\end{enumerate}

\newp

\item You have 200 meters of fencing with which to build two enclosures.
One enclosure will be an isosceles right triangle, and the other will be a rectangle that is three times 
as long as it is wide.  The figure below shows the two shapes.

\begin{tikzpicture}[scale=2]
\draw (0,0) -- (1,0) -- (1,1) -- (0,0);
\draw (2,0) -- (2.5,0) -- (2.5,1.5) -- (2,1.5) -- (2,0);
\end{tikzpicture}


What should the dimensions of the rectangular enclosure be to \textbf{minimize} the combined total area of the two enclosures?



\newp


\item Let $f(x)=\frac{x+5}{x+3}$.  Let $g(x)=f(f(x))$.

\begin{enumerate}
\item Find the asymptotes of $g(x)$.
\vfil
\item Find $g^{-1}(x)$.
\vfil
\item Find the fixed points of $g(x)$.
\end{enumerate}


\newp



\end{enumerate}

\end{document}


% \epsfig{file=pizza01.eps, 
% width=11cm,
% angle=0 }