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Exponential dispersion model; Exponential distribution; Exponential error; Exponential factorial; Exponential family; Exponential field; Exponential formula; Exponential function; Exponential generating function; Exponential-Golomb coding; Exponential growth; Exponential hierarchy; Exponential integral; Exponential integrator; Exponential map ...
The factors range from 0 for no growth to 1 for maximum growth. Actual growth is calculated by the total multiplication of each growth factor. For example, if three factors had a value of 0.5, the actual growth would be: 0.5 × 0.5 × 0.5 = 0.125, which is 12.5% of optimum. If each of the three factors had a value of 0.9 the actual growth would be:
Although growth may initially be exponential, the modelled phenomena will eventually enter a region in which previously ignored negative feedback factors become significant (leading to a logistic growth model) or other underlying assumptions of the exponential growth model, such as continuity or instantaneous feedback, break down.
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.
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:
Exponential growth or exponential decay—where the varaible change is proportional to the variable value—are thus modeled with exponential functions. Examples are unlimited population growth leading to Malthusian catastrophe , continuously compounded interest , and radioactive decay .
Liebig's law states that growth only occurs at the rate permitted by the most limiting factor. [ 2 ] For instance, in the equation below, the growth of population O {\displaystyle O} is a function of the minimum of three Michaelis-Menten terms representing limitation by factors I {\displaystyle I} , N {\displaystyle N} and P {\displaystyle P} .
Limiting factors may be physical or biological. [4]: 417, 8 Limiting factors are not limited to the condition of the species. Some factors may be increased or reduced based on circumstances. An example of a limiting factor is sunlight in the rain forest, where growth is limited to all plants on the forest floor unless more light becomes ...