Answer:
a)
b)
Let's say that
If we multiply the woule equation by k we got:
So then we satisfy that the equation is also logistic since the parameter
c) If we assume that then we have that
And then [tec] kx (a -x) <0[/tex] for any value of
And if that hhapens then the population will tend to 0 for any initial condition established/
Step-by-step explanation:
For this case we have the following logistic equation
Part a
We want to modify our harvesting for this case, so we harvest hx per unit of time for some
So then the model with harvesting who is proportional is given by:
And we can write like this:
Part b
For this case we assume that and we need to show that the equation is still logistic. So we need that the sollowing quantity higher than 0
Let's say that
If we multiply the woule equation by k we got:
So then we satisfy that the equation is also logistic since the parameter
Part c
If we assume that then we have that
And then [tec] kx (a -x) <0[/tex] for any value of
And if that hhapens then the population will tend to 0 for any initial condition established/