If the growth rate of bacteria in a culture medium is directly proportional Question 3. to the difference between the number of bacteria and a certain optimal number P. a) Derive an expression for the number of bacteria P as a function of the time t given that the initial number of bacteria placed in the culture medium is Po and that the constant of proportionality is A. b) How long does it take for the difference in the mumber of bacteria and the optimal number to reduce to 1/4 of the initial difference?

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