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Figure 1: A bi-phasic bacterial growth curve.. A growth curve is an empirical model of the evolution of a quantity over time. Growth curves are widely used in biology for quantities such as population size or biomass (in population ecology and demography, for population growth analysis), individual body height or biomass (in physiology, for growth analysis of individuals).
Biological exponential growth is the unrestricted growth of a population of organisms, occurring when resources in its habitat are unlimited. [1] Most commonly apparent in species that reproduce quickly and asexually , like bacteria , exponential growth is intuitive from the fact that each organism can divide and produce two copies of itself.
In the long run, exponential growth of any kind will overtake linear growth of any kind (that is the basis of the Malthusian catastrophe) as well as any polynomial growth, that is, for all α: = There is a whole hierarchy of conceivable growth rates that are slower than exponential and faster than linear (in the long run).
By now, it is a widely accepted view to analogize Malthusian growth in Ecology to Newton's First Law of uniform motion in physics. [ 8 ] Malthus wrote that all life forms, including humans, have a propensity to exponential population growth when resources are abundant but that actual growth is limited by available resources:
Examples include the use of passive solar and wind energy as elements of design so that the building can be easily adapted to maintain the desired levels of human comfort within the structure. [citation needed] In economics and business, organic growth refers to market growth that has happened gradually, and not through a sudden buyout or ...
Exponential growth cannot continue indefinitely, however, because the medium is soon depleted of nutrients and enriched with wastes. The stationary phase is often due to a growth-limiting factor such as the depletion of an essential nutrient, and/or the formation of an inhibitory product such as an organic acid. Stationary phase results from a ...
Logistic growth is an example for a bounded growth which is limited by saturation: The graph shows an imaginary market with logistic growth. In that example, the blue curve depicts the development of the size of that market. The red curve describes the growth of such a market as the first derivative of the market volume. The yellow curve ...
The standard logistic function is the logistic function with parameters =, =, =, which yields = + = + = / / + /.In practice, due to the nature of the exponential function, it is often sufficient to compute the standard logistic function for over a small range of real numbers, such as a range contained in [−6, +6], as it quickly converges very close to its saturation values of 0 and 1.