\documentclass[12pt]{article}
%\pagestyle{empty}
\textwidth 6.5in
\textheight 9.5in
\topmargin -1in
\oddsidemargin -.1in
\parskip 1ex
\parindent 0em
\usepackage{epsfig}
\usepackage{subfigure}
\begin{document}
\sf
{
Math 120 (Pezzoli)\hfill Name \rule{10pc}{1mm}
\\
Winter  2014\hfill \\
Midterm \#2 \hfill TA:\rule{10pc}{1mm}\\
\\
.\hfill Section:\rule{10pc}{1mm}\\
}
\vskip .1in

\rule{40pc}{2mm}

Instructions: 

\begin{itemize}

\item Your exam contains 4  problems. 
\item Your exam should contain 5 pages; please make sure you
have a complete exam.

\item Box in your final answer when appropriate. 



\item  Unless stated
otherwise, you {\bf MUST} show
work for credit. No credit for answers only. 
If in doubt, ask for clarification. 

\item Your work needs to be neat and legible.

\item You are allowed one
$8.5\times 11$ sheet of  notes (both sides). Graphing calculators
are NOT allowed; scientific 
calculators are allowed. 
\item Round off your answers to 2 decimal places, unless you are asked for exact answers.
\end{itemize}

\rule{40pc}{2mm}
\vskip .25in


Problem \#1 (15 pts) \rule{5pc}{1mm}\hskip 2in
\vskip .2in
Problem \#2 (15 pts) \rule{5pc}{1mm}\hskip 2in
\vskip .2in
Problem \#3 (15 pts) \rule{5pc}{1mm}\hskip 2in
\vskip .2in
Problem \#4 (15 pts) \rule{5pc}{1mm}\hskip 2in

\vskip .5in

TOTAL (60 pts) \rule{8pc}{1mm}

\vfill\eject

\begin{enumerate}


\item Assume Tom invests \$ 5000 at 2\% annual interest compounded continually.
 
\begin{enumerate}
\item How much money will Tom have after 3 years ?
\vskip 1in
\item How long will it take for Tom's investment to double in value ?
\vskip 3in
\item Assume that Bob also invested \$5000 at annual interest  $r$  compounded continuously. Bob's investment doubled in 4 years. What is $r$ ? Give the answer as a decimal.

\end{enumerate}

\newpage


\item Below is the graph of the function $y=f(x)$ on the domain $-2 \leq x \leq 5$

\begin{figure}[ht]
\centering
\includegraphics[scale=0.3]{120mid2.eps}
\label{fig:subfig1}

\end{figure}

\begin{enumerate}
\item[(a)] Which of the graphs below is the graph of $y=2+f(x-1)$ ? Circle the correct graph.

\begin{figure}[ht]
\centering
\includegraphics[scale=0.25]{plot1.eps}
\includegraphics[scale=0.25]{plot2.eps}
\includegraphics[scale=0.25]{plot3.eps}
\end{figure}




\item[(b)] If the domain of $f$ is $ -2 \leq x \leq 5$ what is the domain of the function $\frac{ f(3x)+5}{x-1}$ ?

\vfill

\item[(c)] Compute $f^{-1}(-1)$

\vfill

\item[(d)] If $h(x)=e^{f(x)}$ Which of the values below is closest to   $h^{-1}(2)$ ? Circle the the right answer.

\vspace{0.5 cm} 

0.6  ,-1, 2.5, -2, 3.5

 
\vfill 
\end{enumerate}
\newpage
\item The population of Townsville was 20000 in the year 2000, 30,000 in 2005 and it is expected eventually to approach (but never exceed) 50,000. Measure time in years after 2000 and population in thousands of people. 
Find a linear to linear function P(t) that calculates the population of Townsville at time t and sketch a graph of P(t) for  t $\geq 0$.

\newpage

\item You have 300 m of fence to build two fencing enclosures as in the picture below: the first is a rectangle with one side twice as long as the other side. The second is another rectangle with one side three times as long as the other one. For which value of $x$ is the area of the two enclosure minimum ? 

\begin{figure}[ht]
\centering
\includegraphics[scale=0.3]{mid2.eps}
\label{fig:subfig1}
\end{figure}

\end{enumerate}
\end{document}
