\input{ThisWeek.tex}
\newcommand{\duedate}{Monday, September 15}
\input{../TemplateWeek/AtHomeWork.tex}
\input{Exercises.tex}

%\booltrue{teacher}

Keep in mind that you'll be using your solutions as notes when you take the quiz in recitation, so write down enough information to explain how you solved the problem, not just the final value.

\begin{enumerate}
\item On a given day, the Delaware River has its high tides at 10:30am and 11:00 pm, but every day they move by an hour, so on the second day the high tides are at 11:30am and 12:00 midnight, and so on.  Every low tide has height $0$ feet above MLLW and every high tide has height $8$ feet above MLLW.  Write down a function $h(t)$ which is consistent with this information.
\item There are two colonies of bacteria, each doubling in population every 28 minutes.  At 10:00am, the first colony has 6 million bacteria and the second colony has 1 million bacteria.  (For each of these, if the answer isn't an exact value, make sure to include an exact calculation, not just the number---for instance, $\sin \frac{3}{7}$ is a good answer, $0.4155$ is not.)
\begin{enumerate}
\item How many bacteria are there in the first colony at 10:56am?
\item How many bacteria are there in the first colony at 10:40am?
\item When will there be 48 million bacteria in the first colony?
\item When will there be 9 million bacteria in the first colony?
\item When will there be 1.5 million bacteria in the second colony?
\end{enumerate}
\item Recall that in class, we learned that on January 1, 2010 at midnight, there were 309.3 million people in the US, and the population is growing at 0.8\% per year.  When will there be 350 million people in the US?
\item A pilot needs to begin descending when the plane is 4.5 km above ground.  The \emph{angle of descent} is the angle between the path of the plane and horizontal travel.  (For instance, if the angle of descent is $0$, the plane is not descending at all, while if the angle is $\pi/2$, the plane is traveling straight down.)  What should the angle of descent be so that the plane will travel exactly 200 km diagonally before reaching the ground.  (Your answer will be in terms of trig or inverse trig functions.)
\item If $f(x)=x^2+\ln x$ (with domain $x>0$), what is $f^{-1}(1)$?
\end{enumerate}

\end{document}