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One method of slowing the growth of an insect population without using pesticides is to introduce...

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Advance Math

One method of slowing the growth of an insect population withoutusing pesticides is to introduce into the population a number ofsterile males that mate with fertile females but produce nooffspring. Let P represent the number of female insects ina population and S the number of sterile males introducedeach generation. Let r be the per capita rate ofproduction of females by females, provided their chosen mate is notsterile. Then the female population is related to time tby

t =

P +S
P[(r ? 1)P ? S]
  dP.

Suppose an insect population with 10,000 females grows at a rateof

r = 1.8

and 700 sterile males are added. Evaluate the integral to givean equation relating the female population to time. (Note that theresulting equation can't be solved explicitly for P.Remember to use absolute values where appropriate.)

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