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zoldman
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I am quite sure the first approach is to use partial fractions but I am
unclear how to finish this equation
1/P*dP/dt=b+aP
unclear how to finish this equation
1/P*dP/dt=b+aP
The rest is algebra:zoldman said:I appreciate the confirmation of the partial Fraction step. I arrive at the same situation:
A=1/b and B=-a/b. And I know both a and b from a linear regression.
So substituting back I get
((1/b)/P+((-a/b)/(b+aP)=dt then integrate both sides
(1/b)lnP +(-1/b)ln(b+aP)=t +C
Now my question is here how do I solve for P= f(t).
In this equation, P represents the population, t represents time, b represents the intrinsic growth rate, and a represents the carrying capacity of the environment.
This equation is derived from the logistic growth model, which takes into account the carrying capacity of the environment. It is based on the assumption that as the population grows, it will eventually reach a point where resources become limited and growth slows down.
Solving this equation allows us to predict how a population will change over time, taking into account the effects of both the intrinsic growth rate and the carrying capacity of the environment. It can also help us understand how different factors, such as resource availability or disease, may impact population growth.
This equation assumes that the growth rate and carrying capacity remain constant over time, which may not always be the case in real-world populations. It also does not account for external factors such as immigration or emigration.
This equation is commonly used in population ecology, epidemiology, and other fields to model and predict population growth. It can also be used to inform conservation efforts and manage populations of endangered species.