The sigmoid growth curve
A logistic growth curve is an S-shaped (sigmoidal) curve that can be used to model functions that increase gradually at first, more rapidly in the middle growth period, and slowly at the end, leveling off at a maximum value after some period of time. The initial part of the curve is exponential; the rate of growth accelerates as it approaches the midpoint of the curve. At the midpoint (K/2), the growth rate begins to decelerate but continues to grow until it reaches K which is called the "Carrying Capacity" for the environment.