Hi,
I am trying to find the average growth rate for a population that can be modeled using logistic growth. My problem lies in the fact that it has been ages since I've done any calculus, but here is the setup:
I am trying to find the average growth rate from the present time, t, to infinity, not the current instantaneous growth rate. The logistic expression can be written as dy/dt = ry(1-y), where y = N(t)/K. K and R are constant. If I integrate from t to infinity and then divide by x(t) = t from t to infinity, I should then be able to find the growth rate by dividing the vertical difference by the horizontal difference. This approach to solving the problem would imply that I could simply use l'Hopital's rule, but then why even integrate in the first place if I'm going to end up taking the derivative of what I just integrated?
Any thoughts on how I might solve this problem?
Thanks!
I am trying to find the average growth rate for a population that can be modeled using logistic growth. My problem lies in the fact that it has been ages since I've done any calculus, but here is the setup:
I am trying to find the average growth rate from the present time, t, to infinity, not the current instantaneous growth rate. The logistic expression can be written as dy/dt = ry(1-y), where y = N(t)/K. K and R are constant. If I integrate from t to infinity and then divide by x(t) = t from t to infinity, I should then be able to find the growth rate by dividing the vertical difference by the horizontal difference. This approach to solving the problem would imply that I could simply use l'Hopital's rule, but then why even integrate in the first place if I'm going to end up taking the derivative of what I just integrated?
Any thoughts on how I might solve this problem?
Thanks!