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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) $$C=\frac{\sqrt{M}+\sqrt{A_{0}}}{\sqrt{M}-\sqrt{A_{0}}}$$

#### Topics

Differential Equations

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##### Top Calculus 2 / BC Educators  ##### Heather Z.

Oregon State University ##### Michael J.

Idaho State University Lectures

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### Video Transcript

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#### Topics

Differential Equations

##### Top Calculus 2 / BC Educators  ##### Heather Z.

Oregon State University ##### Michael J.

Idaho State University Lectures

Join Bootcamp