Logistic growth curve

K, logistic growth curve constant K, logistic growth curve constant Volume, allometric exponents Liver Kidney Bone... 

Logistic growth curve, where log Y = A/( + Bpx), such as a population growth curve. 

The degree of nitrification did not increase linearly with residence time, but was more of a step change. The accumulation of nitrified oxygen (N02 +N03 ) was described by a logistic growth curve (20), in the range of residence times 2.1 to 4.1 days ... 

Measurement and Mathematical Fitting of Cell Growth. Richards (1960) used a generalized logistic curve for the mathematical fitting of the growth curve of plants. The equation is ... 

Models available linear, logarithmic, inverse, quadratic, cubic, power, compound. S-curve. logistic, growth, exponential... 

Figure 4. Logistic growth curve fit to hypothetical data.

Figure 1.1 Simulation of (a) logistic (symmetrical) and (b) Gompertz (asymmetrical) growth curves. See equations (1.2.5) and (1.2.6), respectively.

The same conclusions follow from a comparative look at chemistry in relation to the rest of the U.S. labor force. Figure 2.1—6 shows the time series of chemists per 10000 workers - an indicator which a logistic growth curve fits well. The enduring trend is one in which chemists represent an increasing fraction of the labor force. But the rate of that increase is slowing, and past performance suggests a saturation around 15 chemists per 10000 workers. 

From the 1970s onwards, Cesare Marchetti and other system analysts have studied thousands of artifacts, and have discovered that their behaviour is described by the same equations that Lotka and Volterra found for the behaviour of predators and prey. The growth pattern of cars, for example, is a logistic curve. Cars spread in a market exactly as bacteria in a broth or rabbits in a prairie. Cultural novelties diffuse into a society as mutant genes in a population, and markets behave as their ecological niches. But why ... 

Figure 29 Model sulfur isotopic evolution in the course of geologic history. The lower trend (labeled 6 Sred) represents the for sulfides. The upper curves (labeled 6 Sox) are the of marine sulfates. TML and VJ simulations assume a logistic type of continental growth as proposed by Taylor and McLennan (1985) and Veizer and Jansen (1979), respectively. BB simulation assumes an instantaneous generation of continental crust, BB-evol simulation assumes instantaneous continental generation, but with delayed invention of oxygen generating photosynthesis. The Phanerozoic trend as in Figure 30. Dots represent measurements of Precambrian sulfates (Claypool et al, 1980) and the hatched field represents sulfates from Holser et al. (1988) (after Godderis...

It is difficult even to obtain numerical solutions of this equation, in the general case. However, if the kernel is a constant (say ATo) the equation may be solved numerically. Plots of the solution may be found in Davis book (Dl) on p. 418. If Kq — 0, one has the logistic equation. For ATo > 0, a set of curves exhibiting exponential growth, a stationary phase, and a phase of decline are predicted for batch growth. 

Finke. M. D., DeFoliart, G. R., and Benevenga, N. J. (1987a). Use of simultaneous curve fitting and a four-parameter logistic model to evaluate the nutritional quality of protein sources at growth rates of rats from maintenance to maximum gain. J. Nutr. 117,1681-1688. 

Figure 13.5 Dimensionless representation of logistic curve for ceU growth in a batch bioreactor when X /Xq = 100.

Technology growth rates according to the logistics curve may be estimated from the Verhulst equation,... 

To estimate the velocity of human migration one can consider r to be the time between successive generations. A value of r = 25 yr is usually assumed [137]. The growth parameter r can be obtained directly from [256], where the population vs time plot for the United States in the 19th century was fitted to a logistic curve, obtaining r = 0.031 0.001 yr ... 

Such equation, also called S logistic curve is used to describe a process with a low growth which accelerate with time to seem an exponential growth. A 10-year period (2012-2022) is considered to achieve 50% substitution in the conventional market starting from 2012, which roughly implies that over the next decade half a million of square meters of membranes modules could be produced. With such cumulative production around year 2020, the membrane cost per m could reach... 

These growth rates were obtained by application of the compound growth formula to predicted values of the logistic curve shown in Figures 5.2-1 and 5.2-2. The saturation level of 9 900 chemists is the asymptote of the logistic curve (see Appendix E). 

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