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\begin{document}

\vfil \noindent

{\LARGE{
\hfil Math 120 Autumn 2017 \hfil \pp
\hfil Final Exam\hfil  \pp
\hfil December 9, 2017 \hfil \pp
}}

\normalsize
\vfil
\medskip
\hfil Name: \hrulefill \hrulefill \hspace{0.5in} Student ID no. : \hrulefill

\medskip

\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
5 &  10 &    \\ \hline
6 &  10 &    \\ \hline
7 &  10 &    \\ \hline
Total & 70 & \\ \hline 
\end{tabular}
}
\end{center}
\vfil
\begin{itemize}
\item Complete all seven questions. 
\item Show all work for full credit. 
\item The only calculator you may use during this exam is
a TI-30XIIs.
All 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, two-sided, 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 170 minutes to complete this exam. 
\end{itemize}
\vfil
.

\newpage

\begin{enumerate}

% Parametric equations and minimum distance.
\item Chuckster and Jarley are walking around the coordinate plane.\\[.1 in]
Chuckster begins at $(37,-5)$ and walks in a straight line at constant speed towards $(3,-57)$, reaching it in 10 seconds.\\[.1 in]
Jarley begins at $(17,20)$ and walks towards $(50,-36)$ at a speed of $13$ units per second.

\begin{enumerate}
\item Write parametric equations for Chuckster's coordinates after $t$ seconds.
\vfil
\item Write parametric equations for Jarley's coordinates after $t$ seconds.
\vfil
\item When are Chuckster and Jarley closest together?
\vfil
\end{enumerate}

\newpage

% Domain, range, like that one problem from the homework?. Inverses somehow too?
\item For this problem, $f(x)$ is some function, and $g(x) = 2f(-x)-5$.

\begin{enumerate}
\item The table on the right shows some values of $f$. Find $g(g(-2))$.
\vspace{-.3 in}
\begin{flushright}
\begin{tabular}{r|l}
$x$ & $f(x)$\\
\hline
$-2$ & $3$\\
$-1$ & $1$\\
$0$ & $2$\\
$1$ & $4$\\
$2$ & $2$
\end{tabular}
\end{flushright}

\vskip 1 in

\item Explain what transformations are needed to change the graph of $y=f(x)$ into the graph of $y=g(x)$.\\[.1 in]
{\small (Do scratch work here, then fill in the blanks below.}

\vskip 1.7 in

\begin{itemize}
\item First, you \underline{\hspace{4.5 in}}.\\[.3 in]
\item Then, you \underline{\hspace{4.5 in}}.\\[.3 in]
\item Finally, you \underline{\hspace{4.5 in}}.\\[.3 in]
\end{itemize}

\item Suppose that $f(x)$ has domain $(-3,7)$ and range $[1,5]$.\\[.1 in]
Find the domain and range of $g(x)$.

\end{enumerate}

\newpage



\item
Gary the gull is hovering above the Puget Sound.  His height in feet
above the Sound after $t$ seconds is given by the following:

\begin{equation*}
H(t)=
\begin{cases}
40& 0 \leq t \leq 6\\
t^2-22t+136& 6< t \leq 13\\
19& 13< t \leq 15\\
8t-101& 15<t \leq20
\end{cases}
\end{equation*} 

\begin{enumerate}
\item  What is the range of $H$?
\vfill

%\item\Points{4} When is Gary nearest to the water?  What is his height above the water
%at that time?
%\vfill

\item  Another gull, Gertrude, is hovering above the Sound.  Her height is
given by $g(t)=2t+1$.  When are Gertrude and Gary at the same height?
\vfill
\end{enumerate}

\newpage

\item A farming town in Idaho grew 168,000 potatoes in 2008. 
The population of the town that year was 1200. In 2012 the population was 1414. 
%In 2014 they grew 332,000 potatoes.
The number of potatoes the town produces per year doubles every 6 years.

\begin{enumerate}
\item Give an exponential function in the form $y=A b^t$ relating the population $y$ of the town to the year $t$. (Take $t=0$ in 2008).
\vfil

\item Give an exponential function in the form $z=A b^t$ relating the number of potatoes $z$ to the year $t$.
\vfil \vfil

\item In what year will they grow 300 potatoes for each person in the town?
\vfil
\vfil

\end{enumerate}

%\newpage
%
%\item Clovis began his sea shell collection with 5 shells in 1992. In 1996 he had 21 shells and in 2000 he had 45. Take $t=0$ in 1992.
%\begin{enumerate}
%\item\Points{6} Give a linear-to-linear rational function relating the number of sea shells $y$ to the year $t$.\\
%\vfil
%\vfil
%
%\item\Points{3} According to your model, in what year will he have 405 shells in his collection?\\
%\vfil
%
%\item\Points{3} How many shells does he have in 2016?
%
%
%\end{enumerate}

\newpage

\item 
\begin{minipage}[t]{0.6\textwidth}
Isobel is jogging {\bf clockwise} around a circular race track. 
The distance around the track is $\frac{1}{4}$ mile. Isobel jogs at a constant speed of 5 miles per hour. Tafu starts his stopwatch when Isobel is at the due West point on the track. Tafu is standing 10 feet East of the edge of the track. (See the picture.)
\end{minipage}\hfill
\begin{minipage}[b]{0.3\textwidth}
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\draw (0,0) circle (1cm);
\draw[dashed] (-1.3,0) -- (1.3,0);
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\fill[black] (1.2,0) circle (0.04);
\node  at (-1.1,0.15) {I};
\node at (1.2,-0.2) {T};
\end{tikzpicture}
\vspace{-1.2in}
\end{minipage}

\begin{enumerate}


\item
Give parametric equations for Isobel's position as a function of time. Measure distance in feet and time in minutes. (There are 5280 feet in a mile.)
\vfil


\item
After 35 minutes, Isobel stops for a rest. What is her distance from Tafu at this time?
\vfil
\vfil



\end{enumerate}

\newpage

% Triangle trig

\item You're standing in a field thinking about trigonometry when you notice a dinosaur off in the distance, running towards you at a constant speed.\\[.1 in]
Oh no.\\[.1 in]
From your position, the top of the dinosaur's head is at an angle of $4^\circ$ above the horizon.\\[.1 in]
You wait one minute pondering the situation, then measure the angle again. Now it's $6^\circ$!\\[.1 in]
So you run away at a speed of 12 feet per second. One minute later, you measure the angle and find it to be $7^\circ$.\\[.1 in]
This is really bad. How tall is that dinosaur?

\newpage

% Sinusoidal
\item The secret to cooking Sine Stew is to use a special pressure cooker whose pressure varies as a sinusoidal function of time.\\[.1 in]
When you turn on the pressure cooker, it's at a minimum pressure of 10 psi. The pressure then increases until 9 minutes later, when it reaches a maximum of 13 psi.
\begin{enumerate}
\item Write a function for the pressure in the pressure cooker after $t$ minutes.
\vskip 2 in
\item To make the perfect Sine Stew, you must turn off the pressure cooker when the stew has been above 12 psi for exactly 17 minutes.\\[.1 in]
After starting the pressure cooker, how long should you wait before turning it off?
\end{enumerate}


\newpage

\end{enumerate}


\end{document}