A population of zebras is modeled by P(t) which is an initial value problem. Assume t is measured in months. dP dt = P(102-10-8P), P(0) = 20000 b) a) What is the limiting value of the population? After how many months will the population be equal to one quarter of the limiting value in (a)? Do Not round any of your numbers for this question your answer must be exact and symbolically written. Please write neatly so I can understand don't type it in latex. I will give you a like!!

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. Let P represent the number of female insects in a population and S the number of sterile males introduced each generation. Let r be the per capita rate of production of females by females, provided that their chosen mate is not sterile. Then the female population is related to time t by t = ∫(P + S)dP/P[(r-1)P - S]   Suppose an insect population with 10,000 females grows at a rate of r = 1.2 and 900 sterile males are added initially. Evaluate the integral to give an equation relating the female population to time. (Note that the resulting equation cannot be solved explicitly for P.)

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