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{\LARGE{
\hfil Math 120 B - 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}
}
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\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
{\small (Version 1)}

\newp

\begin{enumerate}

\item Jessa is deciding how much to charge for her self-published memoir. The number of copies she sells is a linear function of the amount that she charges.\\[.1 in]
If she charges \$10 per copy, she'll sell 200 copies.\\[.1 in]
If she charges \$30 per copy, she'll sell 140 copies.

\begin{enumerate}
\item Find a function $f(x)$ for the {\bf total amount of money} Jessa earns by charging $\$x$ per copy.
\vfill
\item How much should she charge in order to {\bf maximize} her revenue?
\vfill
\end{enumerate}

\newp

\item 

\begin{enumerate}
\item Suppose $f(x) = \sqrt{x}+2x$, and $g(x) = e^x+3$. Compute $f(g(x))$.
\vskip 2.5 in
\item Suppose $f(x) = \sqrt{x}+2x$. Compute its inverse function, $f^{-1}(x)$.
\vfill
\item Suppose $f(x) = \sqrt{x}+2x$. Give the rule for $h(x)$, whose graph is that of $f(x)$ after being dilated vertically by a scaling factor of 2, and {\em then} translated down 3 units.
\vskip 2.5 in
\end{enumerate}
\newp

\item The cities of Catoma and Vellebue are both growing according to an {\em exponential} model.\\[.1 in]
The population of Catoma was 10,000 in the year 1990 and 14,000 in the year 1998.\\[.1 in]
The population of Vellebue doubles every 15 years. In 2006, it was one quarter of the population of Catoma.
\begin{enumerate}
\item Give a formula $c(t)$ for the number of people in Catoma, $t$ years after 1990.
\vfill
\item Give a formula $v(t)$ for the number of people in Vellebue, $t$ years after 1990.
\vfill
\item In what year will the population of Vellebue be 150,000?
\vfill
\end{enumerate}

\newp

\item The population of the Democratic Republic of Rationalia can be modeled by a {\em linear-to-linear rational function}.\\[.1 in]
In the year 1900, there were 40 million people in Rationalia.\\[.1 in]
In the year 2000, there were 85 million people in Rationalia.\\[.1 in]
In the long term, Rationalia's population will approach (but not exceed) 130 million.
\begin{enumerate}
\item Write a linear-to-linear rational function $f(x)$ for the population of Rationalia, {\bf in millions}, as a function of time. Let $x=0$ represent the year 1900.
\vfil
\item What will the population be in the year 2050?
\end{enumerate}

\end{enumerate}

\end{document}


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