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During lag phase, bacteria adapt themselves to growth conditions. It is the period where the individual bacteria are maturing and not yet able to divide. During the lag phase of the bacterial growth cycle, synthesis of RNA, enzymes and other molecules occurs.
A logistic function or logistic curve is a common S-shaped curve ( sigmoid curve) with the equation. where. is the carrying capacity, the supremum of the values of the function; is the logistic growth rate, the steepness of the curve; and. is the value of the function's midpoint.
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.
The Gompertz curve or Gompertz function is a type of mathematical model for a time series, named after Benjamin Gompertz (1779–1865). It is a sigmoid function which describes growth as being slowest at the start and end of a given time period. The right-side or future value asymptote of the function is approached much more gradually by the ...
Pierre François Verhulst. Pierre François Verhulst (28 October 1804, in Brussels – 15 February 1849, in Brussels) was a Belgian mathematician and a doctor in number theory from the University of Ghent in 1825. He is best known for the logistic growth model.
The generalized logistic function or curve is an extension of the logistic or sigmoid functions. Originally developed for growth modelling, it allows for more flexible S-shaped curves.
With logistic growth, this point, called the maximum sustainable yield, is where the population size is half the carrying capacity (or ). The maximum sustainable yield is the largest yield that can be taken from a population at equilibrium.
After dividing both sides of the equation by the population size N, in the logistic growth the left hand side of the equation represents the per capita population growth rate, which is dependent on the population size N, and decreases with increasing N throughout the entire range of population sizes.