Question

(1 point) Populations of aphids and ladybugs are modeled by the equations d.A 41 = 1.4-0.02.1 L dt dL dt -0.4L +0.004.AL (a). Find the equilibrium solutions. Enter your answer as a list of ordered pairs(A, L), where A is the number of aphids and L the number of ladybugs. For example, if you found three equilibrium solutions, one with 100 aphids and 10 ladybugs, one with 200 aphids and 20 ladybugs, and one with 300 aphids and 30 ladybugs, you would enter (100, 10).(200, 20), (300,30) Do not round fractional answers to the nearest integer. Answer- (b). Find an expression for dL/d.A dL dA

Answer 1

Given that An equalize solution is a solution for which both A and L are constants if A is constant then dA/dt = 0, so the first equation becomes 1A - 0.02AL A (1-0.02 L) = 0 = A = 0 or L = 100, so if A = 0 and is constant then dL/dA = 0, s0, that second equation reduced to 0 = -0.4L + 0.004 AL 0 = -0.4L + 0.004 (0) L B 0 = -0.4 L so L = 0 thus (A, L) = (0, 0) is one equilibrium solution on the other is L = 100 and A is constant then 0 = -0.4 (100)+ 0.02A (100) 0 = -40 + 2A A = -38 these for (A, L) = (-38, 100) is the other equation point (0, 0) , (38) (100)