Finding logistic growth parameters from population and rate data

[amazingAZN]

Hi all, I've got this logistic growth problem that I'm unsure of on how to start. I've read though the textbook but it's just not clicking for me; I missed a day of class and don't have a chance to go to office hours, so any help would be much appreciated.

I've been given a set of values: time, population, and change in population.

The values are as follows, with each value correlation to each time value of course:

T=0.0, P=2.0, dP/dt=0.11
T=37.71, P=14.0, dP/dt=0.62
T=45.05, P=19.0, dP/dt=0.74
T=57.45, P=29.0, dP/dt=0.84

I've been asked to predict population, P at T=10.

A point in the right direction would be great, thanks.

 

[haruspex]

You should quote relevant equations. That should certainly include the ODE for the logistic growth model, and preferably its general solution too. Try the net, e.g. http://www.mathwords.com/l/logistic_growth.htm

 

[epenguin]

Probably you can do this looking at and playing with the numbers but I think it is not a good idea to do it without drawing three graphs.

 

[haruspex]

The differential equation, you will find, has dP/dt as a quadratic function of P. Since you have data values for P and dP/dt, you can use standard curve fitting (least squares) to find the coefficients (http://www.personal.psu.edu/jhm/f90/lectures/lsq2.html). You can then plug those into the solution of the differential equation to find P as a function of t.