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\begin{document}

\noindent
\vfil \noindent
\large
\hfil Math 120 A, B - Winter 2010 \hfil \pp
\hfil Mid-Term Exam Number Two\hfil  \pp
\hfil February 25, 2010 \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.  Graphic 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 You have 100 cm of wire.
You plan to cut the wire into two pieces and make a square and an equilateral triangle.

Useful formula: the area of an equilateral triangle of side length $s$ is
$\dsps \frac{\sqrt{3}}{4} s^2$.

\begin{enumerate}
\item What should the side lengths of the triangle and square be to 
\emph{minimize} the combined area of the square and triangle?
\vfil
\vfil
\vfil
\item What should the side lengths be to \emph{maximize} the combined area of the
square and triangle?

\end{enumerate}

\vfil

\newp


\item Let $f(x)$ be the linear-to-linear rational function with the following properties.

\begin{itemize}
\item It has a horizontal asymptote of $y=40$.
\item Its graph passes through the point $(6,10)$.
\item Its graph passes through the point $(20,18)$.
\end{itemize}

\begin{enumerate}
\item Find $f(x)$.
\vfil \vfil
\item Find the fixed points of $f(x)$.
\end{enumerate}

\newp

\item A small farming town had a population of 800 in 1960.
In 1970, the population was 950.

The town produced 40,000 pounds of potatoes in 1965.  In 1980, they produced
90,000 pounds of potatoes.

Assume that the population of the town and the amount of potatoes produced each year
are exponential functions of time.

When did the town grow 150 pounds of potatoes per person?  Express your answer in 
years after 1960.

\newp

\item Let $\dsps h(x)=\frac{3x}{x-3}$ and $\dsps j(x) = \frac{x}{x+1}$.  

Let $f(x) = h(j(x))$.

\begin{enumerate}

\item Find $f(x)$.

\vfil

\item Find $\dsps f^{-1}(x)$.

\end{enumerate}

\end{enumerate}



\end{document}


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