<p>A population, P(t), satisfies the logistic differential equation dP/dt = (2/3)P(5-P/100). What is lim as t --> infinity P(t)?</p>
<p>I know you're supposed to factor out the 5 to get dP/dt = (10/3)P(1-P/20)</p>
<p>I'm know k = 10/3 and M = 20
I'm trying to plug everything into M/(1+Ae^-kt) where A = (M-Po)/Po
I think Po is initial population, but I don't know where to go from there.</p>
<p>You can’t solve for Po unless they give you some sort of initial condition, or two points that you can use to solve for +C after integration. You can, however, find the limit as the population approaches infinity. If the logistic growth model is dP/dt = kP(L-P), then the limit is L because that is the carrying capacity.</p>
<p>It’s probably too late, but keep in mind that dP/dt = 0 at two places in a logistic curve, generally speaking: at P = 0 and at P = your carrying capacity, L, which is where P(t) heads to as t goes to infinity.</p>