A tissue culture grows until it has a maximum area of M square centimeters The area A(t) of the culture at time t may be modeled by the differential equation where k is a growth constant (a) Show that if we set A u 2 , then Then find the general solution using Separation of Variables (b) Show that the general solution to Eq (7) is dA dt K (1 A) k M

Question: A tissue culture grows until it has a maximum area of M square centimeters. The area A(t) of the culture at time t may be

A tissue culture grows until it has a maximum area of M square centimeters. The area A(t) of the culture at time t may be modeled by the differential equation

dA dt = K (1 - A) k M

where k is a growth constant.
(a) Show that if we set A = u², then

du dt 1 -k 1 2 M

Then find the general solution using Separation of Variables.
(b) Show that the general solution to Eq. (7) is

A(t) = M J Cek/VM)1_ Cek/VM)t + 1

dA dt = K (1 - A) k M

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a Let A u This gives d 2u du so that Eq 7 becomes du 2 ku 127 dt M Now rewrite u ... View full answer

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