The discussion revolves around a logistic equation modeling population growth, specifically examining the limit of the population as time approaches infinity. Participants are analyzing the implications of initial conditions on the limit of the population function.
The discussion is active, with participants offering different perspectives on the implications of initial conditions and the nature of the solutions to the differential equation. Some guidance has been provided regarding the behavior of the solution as time approaches infinity, but there is still confusion about the initial population's role in determining the limit.
Participants are navigating the constraints of the logistic model, particularly the assumption that a population cannot grow from an initial value of zero. There is an ongoing debate about the interpretation of constants in the solution and their impact on the limit.
No, it's not. As fightfish said, Ae-.5t goes to 0 as t approaches infinity. This, however, does not imply that A is 0 or is approaching zero. A is a constant in the problem.nietzsche said:OH. so now if we take the limit, as t approaches infinity, then A will go to 0, no matter what. is that correct?