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\noindent {\bf Problem statement} A tissue culture grows until it has
an area of 9 cm$^2$. Let $A(t)$ be the area of the tissue at time
$t$. One model for the growth rate is $ A'(t)=k\sqrt{A(t)}\Bigl(9-A(t)\Bigr) $
for some constant $k$. This is reasonable because the number of cells
on the edge is proportional to $\sqrt{A(t)}$ and most of the growth
occurs on the edge.

\medskip

\noindent a) Without solving the equation, show that the maximum rate
of growth occurs at any time when $A(t)=3$ {cm$^2$.

\medskip

\noindent b) Assume that $k=6$. Find the solution corresponding to
$A(0)=1$ and sketch its graph.

\medskip

\noindent c) Do the same for $A(0)=4$.










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