Chapter 7.4, Problem 67E

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. (The photo shows a screw-worm fly, the first pest effectively eliminated from a region by this method.)

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

$t={\displaystyle \int \frac{P+S}{P\left[\left(r-1\right)P-S\right]}}dP$

Suppose an insect population with 10,000 females grows at a rate of r = 1.1 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 can’t be solved explicitly for P.)