8.2-3a) Assume that m(p) = a + bp for some constants a,b>0. That is, the extinction rate increases withp because of competition between subpopulations, but m(p) does notdpvanish as p→0. The model for proportion of occupied sites isdt= cp(1 - p) - (a + bp)p. Assuming that the subpopulations obey the differential equation and thecoefficients are a = 4, b = 1, but c is allowed to take any value, complete parts (a) through (c).(a) Find the equilibrium values of p (your answer will depend on the unknown coefficient c).The equilibrium values are p=(Simplify your answer. Use a comma to separate answers as needed.)

Name: 8.2-3a) Assume that m(p) = a + bp for some constants a,b>0. That is, t
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Description: 8.2-3a) Assume that m(p) = a + bp for some constants a,b>0. That is, the extinction rate increases withp because of competition between subpopulations, but m(p) does notdpvanish as p→0. The model for proportion of occupied sites isdt= cp(1 - p) - (a

dpdt= cp(1-p) - (a+bp)pGiven a=4, b=1dpdt = cp(1-p) - (4+p)pa E cuilibtcium rotution are given by…

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Assume that m(p) = a + bp for some constants a,b > 0. That is, the extinction rate increases withp because of competition between subpopulations, but m(p) does not dp vanish as p→0. The model for proportion of occupied sites is = cp(1 - p) - (a + bp)p. Assuming that the subpopulations obey the differential equation and the cofficients are a = 4, b = 1, but c is allowed to take any value, complete parts (a) through (c). (a) Find the equilibrium values of p (your answer will depend on the unknown coefficient c). The equilibrium values are p = (Simplify your answer. Use a comma to separate answers as needed.)

Assume that m(p) = a + bp for some constants a,b > 0. That is, the extinction rate increases withp because of competition between subpopulations, but m(p) does not dp vanish as p→0. The model for proportion of occupied sites is = cp(1 - p) - (a + bp)p. Assuming that the subpopulations obey the differential equation and the cofficients are a = 4, b = 1, but c is allowed to take any value, complete parts (a) through (c). (a) Find the equilibrium values of p (your answer will depend on the unknown coefficient c). The equilibrium values are p = (Simplify your answer. Use a comma to separate answers as needed.)

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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8.2-3a)

Assume that m(p) = a + bp for some constants a,b>0. That is, the extinction rate increases withp because of competition between subpopulations, but m(p) does not
dp
vanish as p→0. The model for proportion of occupied sites is
dt
= cp(1 - p) - (a + bp)p. Assuming that the subpopulations obey the differential equation and the
coefficients are a = 4, b = 1, but c is allowed to take any value, complete parts (a) through (c).
(a) Find the equilibrium values of p (your answer will depend on the unknown coefficient c).
The equilibrium values are p=
(Simplify your answer. Use a comma to separate answers as needed.)

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