In a laboratory experiment, the population P of a microorganism is found to satisfy the differential equation dP - (15-₁ +1) P dt where t > 0 is the number of hours after the start of the experiment. (a) If the initial population of the microorganism is P = 1000, find P(t). (b) Approximate the population of the microorganism after 30 minutes. Round off your answer to the nearest integer.

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