- #1
agentsanta
- 10
- 0
Hey, I am doing a project on population growth modelling, and I have hit a brick wall in trying to derive a function to represent an aspect of my population
I understand that the derivative of a logistic function is
P'(t)=P(t)(1-P(t))
and from there one can obtain the function P(t)= 1/(1+e^(-t))
However, it seems that the logistic function is too simple for my purposes and I need a function with the following derivative
P'(t)=P(t)(1-P(t)) - P(t-a)(1-P(t-a)) where a is a constant
My problem is to find the function with the above derivative
Anyone have ideas?
I've literally sat down and stared at this thing for the last week and got nothing.
FYI I'm at a senior grade high school level
I understand that the derivative of a logistic function is
P'(t)=P(t)(1-P(t))
and from there one can obtain the function P(t)= 1/(1+e^(-t))
However, it seems that the logistic function is too simple for my purposes and I need a function with the following derivative
P'(t)=P(t)(1-P(t)) - P(t-a)(1-P(t-a)) where a is a constant
My problem is to find the function with the above derivative
Anyone have ideas?
I've literally sat down and stared at this thing for the last week and got nothing.
FYI I'm at a senior grade high school level