- 15 A A Population Study Is Conducted On A New Colony Of Invasive Insects The Study Finds That Initially There Are 60 1 (124.23 KiB) Viewed 32 times
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15. a. A population study is conducted on a new colony of invasive insects. The study finds that initially there are 60 of the insects in 1 m², P(0) = 60. Two weeks later a survey finds 80 of the insects in 1 m², P(2) = 80. Assume that this insect population is growing according to a Malthusian growth law: dP =rP, dt where t is in weeks. Solve this differential equation, find the growth constant r, and determine how long it takes for the total population to double. b. It is found that a predator is adapting to the new invasive insect and is learning to control this pest. A survey after four weeks finds the population has only increased to 90, P(4) = 90. The result is a declining growth rate and a better model for the population is given by the differential equation: dP = (a - bt) P. dt Solve this differential equation. Use the data at t= 0, 2, and 4 weeks to find the constants a and b. Determine the time for this population to reach its maximum and what the maximum population is predicted to be.