Nonlinear models- Logistic Equation?

Question

The number N(t) of people in a community who are exposed to a particular advertisement is governed by the logistic equation. Initially,

N(0)=500, and it is observed that N(1)=1000. Solve for N(t) if it is predicted that the limiting number of people in the community who will see the advertisement is 50, 000.

Can someone help me to form the logistic equation. Please.

Thanks a lot!!!

Answer 1

dN / dt = k N [ 50000 - N ], N(0) = 500 & N(1) = 1000 will help you find k and the constant of integration...I assume you can do partial fractions for integration

Answer 2

I could go through the entire derivation of the logistic equation, but I don't know your background.  If you are taking ordinary differential equations, then you can see the derivation of the logistic equation (and examples of how to fit data to the curve) at http://mathdl.maa.org/mathDL/4/?pa=conte...