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. Letr 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 P+S t-/p | P[(r = t= (r - 1)P - S dP. Suppose an insect population with 10,000 females grows at a rate of r= 1.5 and 400 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.) t-In P + 3 ln P - 800] -18.17
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. Letr 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 P+S t-/p | P[(r = t= (r - 1)P - S dP. Suppose an insect population with 10,000 females grows at a rate of r= 1.5 and 400 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.) t-In P + 3 ln P - 800] -18.17
Chapter6: Exponential And Logarithmic Functions
Section6.8: Fitting Exponential Models To Data
Problem 3TI: Table 6 shows the population, in thousands, of harbor seals in the Wadden Sea over the years 1997 to...
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Transcribed Image Text: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 =
t =
P + S
P (r - 1)P - S
I
dP.
Suppose an insect population with 10,000 females grows at a rate of r = 1.5 and 400 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.)
-In|P| +3 ln | P – 800| – 18.17
X
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