Question

Scientists studying a population of wolves (y), and a population of rabbits (x) on which the wolves depend for food, have found the sizes x and y of these populations to be modeled well by the equation 4 Iny -0.02y +3 In x -0.001x = 37.37 P(5000,300) wolves [The equation is graphed at right. Point P(x, y) moves around the curve in the direction shown as x and y variously increase and decrease in what is known as a predator-prey cycle. It takes a little over 7 years here to complete a cycle.] 2.000 3.000 4.000 5.000 6,000 rabbits [6] [3] The scientists have estimated the current population sizes to be x = 5000 rabbits and y-300 wolves, with the number of rabbits decreasing right now at the rate of 2500 rabbits per year. (a) Find at the point P45000,300). (b) Find the rate at which the wolf population is increasing right now

Answer 1

Answers Given that hot scintists studling a papulation of wolves (Y) and population of sabbits G) we have found the sizes acandy Now, ulny-0.02% 43 lnx-o.cold = 37.37 differsatative with respect to a sky-bole to-0-00) = 0 glyco.c01-22 de (42002) (sce,100) => day (0.001 -0.0005) a cu o -0.02] des dx=2500 dy = -3 (-250) = 150 dy = 150 population increas by 150 per year the above problem solved Hence