\subsection{Exercise for Homework 3}\label{M4_P2_HW3}
\begin{enumerate}
\item Another factory runs on on 4 hour shifts and the concentration
function is $c(t)=3.2t(4-t)e^{-2.5(4-t)t}$. The flow rate is 100
L/hour. 
\begin{enumerate}
\item What is the total amount of chemical to flow into the tank in
the first 2 hours of the shift?
\item What is the total amount of chemical to flow into the tank in a shift?
\item A full tank holds 1600L. What is the  mass of the chemical in a full
  tank?
\end{enumerate}
\item At another factory the concentration function, for a 6 hour
shift, is know to be $c(t)=3(6-t)e^{-0.01(6-t)}$. The flow rate is 200
L/hour. 
\begin{enumerate}
\item State the differential model for $A(t)$, the total amount of
chemical to flow out in the first $t$ hours of the shift.
\item Find the increase in the amount of chemical to flow into the
  tank between the second and fifth hour of the shift.
\end{enumerate}
\end{enumerate}
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