Question

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 their chosen mate is not sterile. Then the female population is related to time t by

Answer 1

P + S / P [(r - 1) P - S] dP

Explanation:

If r = 0.10 and S = 900 then,

P + 900 / P [(0.10 - 1) P - 900] dP

Solving the equation we get,

P + 900 = (B - 0.9A)P - 900A

If A = -1,

B = 0.10

t = 0 and P = 10,000

ln 10000 - 1 /9 ln (0.9 * 10000 + 900) + C

C = 10.2326.