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\begin{document}

\noindent \vfil \noindent \large \hfil Math 120 A Spring 2011 \hfil \pp \hfil Mid-Term
Exam Number Two\hfil  \pp \hfil May 19, 2011 \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 Over time, Frank's accuracy at the game of darts gets better and better. When Frank
was 20 years old, he was only 62 percent accurate. When he was 30 years old, he was 85
percent accurate. Assume that his accuracy will always increase, and will approach
arbitrarily close to 100 percent if he lives long enough. Suppose Frank's accuracy
percentage is a linear-to-linear function of his age. How old will Frank be when he is 95
percent accurate?

\newp

\item Let $f(x)=x+2|x-3|$, and $g(x)=3x-1$.

\begin{enumerate}
\item Find all solutions to the equation $f(g(x))=-4x$.

\vfil

\item Let $h(x)=g(\sqrt{x})+x+1$.  Find $h^{-1}(x)$.

\end{enumerate}

\newp

\item The population of the city of Gub has a doubling time of 63 years. 
In 1990, Gub's population was 20,000, while the city of Lok's population was 10,000. 
In 2005, Gub's population was 50 percent more than the population of Lok in 2005. 

Assuming Lok's population is growing exponentially, 
when will the cities have equal populations?  Express your answer in years after 1990.

\newp

\item Each of the wheels of a bicycle has a radius of 32 cm.
The rear sprocket has a radius of 3 cm.  What radius should the front sprocket have
to achieve a speed of 30 km per hour while pedaling at 100 rpm (revolutions
per minute)?

 \epsfig{file=bike01.eps, 
 width=11cm,
 angle=0 }

\end{enumerate}

\end{document}


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