One method of slowing the growth of an insect population without using pesticides is to introduce into the population a number of sterile males that mate with fertile females but produce no offspring. If P represents the number of female insects in a population, S the number of sterile males introduced each generation, and r the population's natural growth rate, then the female population is related to time t by

Suppose an insect population with 10,000 females grows at a rate of r = 0.10 and 900 sterile males are added. Evaluate the integral to give an equation relating the female population to time.

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P+ S dP