💬 👋 We’re always here. Join our Discord to connect with other students 24/7, any time, night or day.Join Here!

Oh no! Our educators are currently working hard solving this question.

In the meantime, our AI Tutor recommends this similar expert step-by-step video covering the same topics.

Let $A(t)$ be the area of a tissue culture at time $t$ and let $M$ be the final area of the tissue when growth is complete. Most cell divisions occur on the periphery is proportional to $\sqrt {A(t)}.$ So a reasonable model for the growth of tissue is obtained by assuming that the rate of growth of the area is jointly proportional to $\sqrt {A(t)}$ and $M - A(t).$(a) Formulate a differential equation and use it to show that the tissue grows fastest when $A(t) = \frac {1}{3} M.$ (b) Solve the differential equation to find an expression for $A(t).$ Use a computer algebra system to perform the integration.

a) $$=\frac{1}{2} k A^{-1 / 2}[k \sqrt{A}(M-A)][M-3 A]=\frac{1}{2} k^{2}(M-A)(M-3 A)$$b) $$C=\frac{\sqrt{M}+\sqrt{A_{0}}}{\sqrt{M}-\sqrt{A_{0}}}$$

Discussion

You must be signed in to discuss.
Anna Marie V.

Campbell University

Heather Z.

Oregon State University

Michael J.

Idaho State University

Boston College

Lectures

Join Bootcamp

Video Transcript

are a where the on the d r a The in the bond needy My my a one thing is given as he way last over who are a gay three. No, we have And And the bar it the deity supposed todo is he would One day, that is we have been related in my view. Zero. So that gives us and upon to the weather it ah e one it goes may have seen that they needed into the upon it we pursue This is possible when Ben A No, they that mais the last well right is a one of the no. Uh, but be off the problem it he wouldn t o Why don't and Z plus Katie, This is the answer about me on the bench. That's a

Other Schools

Topics

Differential Equations

Anna Marie V.

Campbell University

Heather Z.

Oregon State University

Michael J.

Idaho State University

Boston College

Lectures

Join Bootcamp