If someone wants to know how to predict the cumulative of a logistics curve when the data is still around the inflection point but before the asymptote is reached, there's a technique one can borrow from the fossil fuel resource world called *Hubbert linearization*. This is a screen grab from the book that shows how the HL is graphically constructed. The value of dU/U is plotted against U (as in eq 7.8) and the x-intercept gives the asymptotic limiting value. Wikipedia explanation : https://en.wikipedia.org/wiki/Hubbert_linearization
This only works for the case of the perfect logistic, and any other (non-exponential) growth law won't linearize in the same way, as is seen in a power-law growth model.