I have the equation dP/dt = kP(1 - P/A). It is supposed to describe a logistical situatuon involving the carrying capacity of the system. k is a constant, and A is the carrying capacity of the system. t is time and P is population as a function of time. P(0) = P0. I solved c (the integration constant) to be: c = -ln|(P0)/(A - P0)| I'm trying to solve the equation in terms of t. In my calculus book, a similar equation is given with an explanation. dP/dt = 0.1P(1 - P/300) With an initial condition of P(0) = 50, c is found to be ln(1/5). A = 300 and k = 0.1. I follow along well up to this point. After solving for c, the book lists the rearranged equation as: P(t) = 300/(1 + 5e-0.1t) I don't understand how they went from one equation to the other, the closest I could come with the general equation was: P(t) = (Aekt + Q)/(1 + ekt) where Q = (P0)/(A - P0) Which would coincide with an equation of: (300e0.1t + .2)/(1 + e0.1t) Which, when graphed, is not equivalent to the equation given by the book. Can anyone go over how to solve the general equation? I think I'm missing some crucial point. Thank you!