T issue culture Let Astd 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 of the tissue and the number of cells on the periphery is proportional to sAstd. 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 sAstd and M 2 Astd.

(a) Formulate a differential equation and use it to show that the tissue grows fastest when Astd − 13 M.

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(b) Solve the differential equation to find an expression for Astd. Use a computer algebra system to perform the integration.