Help with logistic growth problem

[amazingAZN]

Hi all, I've got this logistic growth problem that I'm unsure of on how to start. 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.

 

[pasmith]

Hi all, I've got this logistic growth problem that I'm unsure of on how to start. 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.

The ODE you are trying to solve is
$$\frac{dP}{dt} = kP(P_0 - P)$$
for some constants $k$ and $P_0$ which you can estimate from the given data for $dP/dt$ and $P$.