Let be the area of a tissue culture at time and let be the final area of the tissue when

Chapter 9, Problem 43

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Let be the area of a tissue culture at time and let be the final area of the tissue when growth is complete. Most cell divisions occur on the periphery of the tissue and the number of cells on the periphery is proportional to . So a reason- able model for the growth of tissue is obtained by assumingthat the rate of growth of the area is jointly proportional toand .(a) Formulate a differential equation and use it to show thatthe tissue grows fastest when .(b) Solve the differential equation to find an expressionfor . Use a computer algebra system to perform theintegration.

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