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## Homework 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. A model of the growth rate is that:

A'(t) = k*(sqrt(A(t)) * (9-A(t))

a. Without solving the equation, show that the maximum rate of growth

occurs at any time when A(t) = 3 cm^2.

b. Assume that k = 6. Find the solution corresponding to A(0) = 1 and

sketch its graph.

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

## Homework Equations

y(t) = b + e^kt ?

## The Attempt at a Solution

For part A, I took the derivative and set that equal to 0, which gave me back 3.

For part B, i took it as a separable differential equation and got

(1/3)(ln((9-A)/(3-sqrt(A))^2)) = kt + C

but i have no idea how to solve that for A

Thanks for any help