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exponential growth

exponential growth A form of population growth in which the rate of growth is related to the number of individuals present. Increase is slow when numbers are low but rises sharply as numbers increase. If population number is plotted against time on a graph a characteristic J-shaped curve results (see graph). In animal and plant populations, such factors as overcrowding, lack of nutrients, and disease limit population increase beyond a certain point and the J-shaped exponential curve tails off giving an S-shaped (sigmoid) curve.

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exponential growth

exponential growth A form of growth in which the logarithms of a value increase linearly in any given period of time. This means that the value grows more rapidly than it would by linear growth. An example of exponential growth would be a population that grows by 10 per cent of its value in each unit of time. Thus, a population that starts with a value of 100 would grow as: 100, 110 (100 + 10% of 100), 121 (110 + 10% of 110), 132.1 (121 + 10% of 121), …

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exponential growth

exponential growth The exponential family of curves (Y = ex) describes growth at an increasing (geometrical) ratio (as in the example of compound interest rates). Thomas Malthus (Essay on the Principle of Population, 1789) pointed out that if food resources increase in linear (arithmetical) ratio, and population increases exponentially, extinction is inevitable. A more descriptive model for growth is logistic. See also LOGISTIC GROWTH.

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