PLEASE HELP! Equilibria and Stability: Suppose that a population study on Pygmy
ID: 2998795 • Letter: P
Question
PLEASE HELP! Equilibria and Stability:Suppose that a population study on Pygmy Rabbits in a particular region finds that the population, P(t), of the Pygmy Rabbits satisfies the differential equation:
dP/dt=P(r-a(P-b)^2)
Where r=.4 , a=.02 , and b=50. Find the equilibria for this differential equation.
a. Determine the stability of the equilibria of this model
b. Describe what happens to the following starting populations of the Pygmy Rabbits as predicted by this model.
i. 20
ii. 50
iii. 80
iv. 100
Explanation / Answer
for equilibrium dp/dt =0 ie P(r-a(p-b)^2)=0 hence (p-b)^2 =r/a =20 hence p = 54.47 or p = 45.53