Hey Guys,
I'm doing a question related to logistic model with harvesting.
It goes as follows:
Fishery A uses the following model for the absolute growth rate
dP/dt= r P(1-P/K)-h
where h is the constant absolute harvest rate.
(a)If r = 1.04 and K = 100 calculate the harvest rate h which gives
an equilibrium at Peq = 55.
(b)Using the above values of r, K and h show that the model can be
rewritten in the factorised form
dP/dt=r/K(P ? a)(b ? P).
and find the values of a and b.
By my calculations h = 25.74
But I'm having trouble working out how they got to the factorised form. I haven't done maths in ages so I'm a bit scratchy on factorization, which may be where my problem lies. I specifically don't understand where the h dissapeared to. What also confuses me is I dont understand how you can introduce a and b- which I thought is what you do when using the partial fraction technique and seperation of variable technique- when this problem doesnt seem to be a fraction or, in their factorised form, have the variables separated.
Sorry if that confusing, but I guess it's a reflection of my general attitude toward this question!
Would be really appreciative if anyone could point me in the right direction!
Cheers,
I'm doing a question related to logistic model with harvesting.
It goes as follows:
Fishery A uses the following model for the absolute growth rate
dP/dt= r P(1-P/K)-h
where h is the constant absolute harvest rate.
(a)If r = 1.04 and K = 100 calculate the harvest rate h which gives
an equilibrium at Peq = 55.
(b)Using the above values of r, K and h show that the model can be
rewritten in the factorised form
dP/dt=r/K(P ? a)(b ? P).
and find the values of a and b.
By my calculations h = 25.74
But I'm having trouble working out how they got to the factorised form. I haven't done maths in ages so I'm a bit scratchy on factorization, which may be where my problem lies. I specifically don't understand where the h dissapeared to. What also confuses me is I dont understand how you can introduce a and b- which I thought is what you do when using the partial fraction technique and seperation of variable technique- when this problem doesnt seem to be a fraction or, in their factorised form, have the variables separated.
Sorry if that confusing, but I guess it's a reflection of my general attitude toward this question!
Would be really appreciative if anyone could point me in the right direction!
Cheers,