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\textbf{Math 220 \hfill Quiz 8 (take-home) \hfill Spring 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 (give 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 and the textbook.
\item You should not use a calculator except to do basic arithmetic.
\item Show sufficient work to justify each answer.
\item The quiz should be turned in to your TA by 1pm Friday. If you will not see your TA then you can submit it to your TA's mailbox in 250 Altgeld.
\item Be sure that the pages are nicely stapled -- don't just fold the corners.
\item Note to TA's -- you should not help students with these specific problems or go over solutions until after 1pm Friday.
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\item (2 points) There are currently $50$ rabbits living on Lady Tottington's Estate. Suppose $\D{\frac{dR}{dt} = 0.04R}$ where $R$ represents the number of rabbits on the estate $t$ months from now.
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\item Find a formula for $R$ as a function of $t$.
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\item In how many months will there be $150$ rabbits living on the estate?
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\item (3 points) If a box must have a square end then what dimensions will give the box of greatest volume which can be shipped via Priority Mail? The U.\ S.\ Postal Service will accept a box for shipment via Priority Mail only if the combined length and girth (distance around) is no more than $108$ inches.
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\item (2 points) A function $f$ has second derivative $\D{f''(x) = (x-1)^4(x-2)^7(x^2-25)}$. Determine the $x$-value for each inflection point on the graph of $f$.
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\item (3 points) A ladder $12$ feet long rests against a vertical wall. If the bottom of the ladder slides away from the wall at a rate of $0.5$ feet per second, how quickly in radians per second is the angle between the ladder and the wall increasing when the bottom of the ladder is $5$ feet from the wall?
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