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\textbf{Math 220 \hfill Quiz 2 (take-home) \hfill Fall 2010} \\
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\textbf{Your Name}\ \rule{3.5in}{.4pt} \hfill \\[0.3in]
\textbf{TA's Name}\ \rule{3.5in}{.4pt} \hfill \\[0.3in]
\textbf{Discussion Section}\ \rule{3.5in}{.4pt} \hfill \\ \hspace*{0.3in} \textrm{\small (list either section number or meeting times)} \\[0.3in]
\begin{itemize}
\item You may work with other students in this class. However each student should write up solutions separately and independently -- nobody should copy someone else's work.
\item You may use your notes or the textbook.
\item No calculators are allowed on any problem except \#1
\item You must show sufficient work to justify each answer.
\item The quiz should be turned in to your TA by 4pm Thursday. You are allowed to turn it in early when you next see your TA. Although most TA's mailboxes are in 250 Altgeld your TA should inform you about the best way to submit your quiz.
\item Be sure that the pages are nicely stapled -- do not just fold the corners.
\item Note to TA's -- you should not help students with these specific problems or go over solutions until after 4pm Thursday.
\end{itemize}
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\begin{enumerate}
\item (3 points) Let $P(t)$ represent the population of rabbits in a prairie $t$ months since observation began. Fill in the missing entries $P(1)$, $P(2)$ and $P(3)$ given that the population grows exponentially. You may use a calculator for this problem, but you must still show sufficient work to justify your answers.\\[0.2in]
\begin{tabular}{c|c}
$t$ & $P(t)$ \\ \hline
$0$ & $200$ \\ \hline
$1$ & \\ \hline
$2$ & \\ \hline
$3$ & \\ \hline
$4$ & $1000$ \\
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\item (2 points) Determine the exact value for each solution to the equation below.
$$\ln{\left(4-x\right)} + \ln{\left(4+x\right)} = 0$$
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\item (2 points) Find the domain of the function $\D{f(x) = \frac{e^{2x}+9}{e^{2x}-100}}$
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\item (2 points) Given that $\D{f(x) = \left(\ln{\left(2x - 5\right)}\right)^{3}}$, find a formula for $\D{f^{-1}(x)}$.
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\item (1 point) Given that $f$ is a one-to-one function determine the value of $\D{f^{-1}(5)}$ given that
$$f(-5)=-10, f(-3)=-5, f(3)=5 \mbox{ and } f(5)=10$$
\end{enumerate}
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