“exponential growth”的概念、定义、翻译、参考文献-科学参考

exponential growth

Physics

A form of growth in, for example, a population 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.

Exponential growth. Graph showing exponential growth of the human population.

Mathematics

If y = Ae^kt, where A>0 and k>0 are constants, and t denotes time, y is said to be exhibiting exponential growth. This occurs when dy/dt = ky; that is, when the rate of change of the quantity y at any time is proportional to the value of y at that time. Any quantity with exponential growth ultimately outgrows any polynomial growth. Compare exponential decay.

Chemical Engineering

The growth of a microorganism in a culture that is unrestricted in terms of nutrients or substrate such that there is a repetitive doubling. The increase in population is:
$\frac{d N}{d t} = k N$

Integrating from an initial population N_o at time t = 0, gives N = N_oe^kt. In practice, the nutrient or substrate is limiting and the growth curve is not indefinitely exponential but sigmoidal or S-shaped.

Biology

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.
Graph showing exponential growth of the human population

单词	exponential growth
释义	exponential growth Physics A form of growth in, for example, a population 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. Exponential growth. Graph showing exponential growth of the human population. Mathematics If y = Ae^kt, where A>0 and k>0 are constants, and t denotes time, y is said to be exhibiting exponential growth. This occurs when dy/dt = ky; that is, when the rate of change of the quantity y at any time is proportional to the value of y at that time. Any quantity with exponential growth ultimately outgrows any polynomial growth. Compare exponential decay. Chemical Engineering The growth of a microorganism in a culture that is unrestricted in terms of nutrients or substrate such that there is a repetitive doubling. The increase in population is: $\frac{d N}{d t} = k N$ Integrating from an initial population N_o at time t = 0, gives N = N_oe^kt. In practice, the nutrient or substrate is limiting and the growth curve is not indefinitely exponential but sigmoidal or S-shaped. Biology 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. Graph showing exponential growth of the human population
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