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**logistic**function or**logistic**curve is a common S-shaped curve ( sigmoid curve) with equation where , the value of the sigmoid's midpoint; , the supremum of the values of the function; , the**logistic****growth**rate or steepness of the curve. [1]A Malthusian

**growth**model, sometimes called a simple exponential**growth**model, is essentially exponential**growth**based on the idea of the function being proportional to the speed to which the function grows.The

**logistic****growth**curve depicts how population**growth**rate and carrying capacity are inter-connected. As illustrated in the**logistic****growth**curve model, when the population size is small, the population increases exponentially. However, as population size nears carrying capacity, the**growth**decreases and reaches zero at K. [24]The

**logistic**model (or**logistic**function) is a function that is used to describe bounded population**growth**under the previous two assumptions. The**logistic**function is bounded at both extremes: when there are not individuals to reproduce, and when there is an equilibrium number of individuals (i.e., at carrying capacity ).The

**logistic**model takes the shape of a sigmoid curve and describes the**growth**of a population as exponential, followed by a decrease in**growth**, and bound by a carrying capacity due to environmental pressures. [4]The generalized

**logistic**functionor curveis an extension of the logisticor sigmoidfunctions. Originally developed for**growth**modelling, it allows for more flexible S-shaped curves. The function is sometimes named Richards's curveafter F. J. Richards, who proposed the general form for the family of models in 1959.**Definition**[edit]The

**logistic****growth**equation is an effective tool for modelling intraspecific competition despite its simplicity, and has been used to model many real biological systems. At low population densities, N (t) is much smaller than K and so the main determinant for population**growth**is just the per capita**growth**rate.