S-Curve

curve with growth followed by levelling off

Sigmoid Function http://en.wikipedia.org/wiki/Sigmoid_function

Logistic Curve/Logistic function https://en.wikipedia.org/wiki/Logistic_function The logistic function was introduced in a series of three papers by Pierre François Verhulst between 1838 and 1847, who devised it as a model of population growth by adjusting the exponential growth model, under the guidance of Adolphe Quetelet.[5] Verhulst first devised the function in the mid 1830s, publishing a brief note in 1838,[1] then presented an expanded analysis and named the function in 1844 (published 1845);[a][6] the third paper adjusted the correction term in his model of Belgian population growth.[7] The initial stage of growth is approximately exponential (geometric); then, as saturation begins, the growth slows to linear (arithmetic), and at maturity, growth stops.

Life Cycle model?

Looks like Increasing Returns until you're halfway up.