A growth curve in which the rate of growth is proportional to the product of the size at the time and the amount of growth remaining. It has an S-shaped or sigmoid curve, indicating little growth, followed by a sudden spurt to an asymptote, and has been used to identify continuous accelerations in the development of particular behaviors. Known also as the Verhulst model after the mathematician Pierre F. Verhulst (1804-1849) who introduced the model for the function in 1845. He used the model to predict the US population in 1940 using census data from 1790 to 1840 and was only off by less than 1%. However, the model did not predict the census results after 1940 for growth in the US population, probably due to the effects of the Second World War.
See Asymptote, Exponential, Growth-mixture model