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South Carolina Population History
This example shows that it is possible to use the Constant Rateversion of the Malthusian Growth Model and maintain a state of perpetualexponential growth. Okay, so it requires the constant rate to switch betweenpositive and negative rates, but it's much closer to what Malthus proposed thanhe is usually given credit for. Most writers limit their arguments to dismissingMalthus on the grounds that a population cannot grow endlessly at a constant positiverate of growth. Rather than dismissing Malthus, they prove their own inabilityto appreciate the true nature of the (so I've given it anew name, the ). Now, pure constant rate exponential growth is explored via theMalthusian Growth Model, and variable rate exponential growth (specificallycatering for both positive and negative rates) is explored via the CouttsianGrowth Model.
Project 2001: Significant Works in Economic History
The Malthusian Growth Model is only in troubleif the constant rate of growth is positive. It is in trouble because, as Malthushimself helped to point out (see ), any population which sustains positive populationgrowth could fairly quickly cover the Earth  clearly an absurdity! However, if the upper growth limit is reached, simply invoke a negative rate of growth to reduce the population below the . The negative rate of growth could be a constant rate, even thesame absolute value as the previous positive rate used to reach the limit togrowth. This is roughly what Malthus expected.
Simon Kuznets, Modern Economic Growth: Rate, Structure and Spread
The true nature of the exponential growth of populations does not reveal itself until of growth are considered. In fact, Logistic Growth uses variable rates of growth whichare inexorably tied to the .
Economic Growth  Our World in Data
Malthus took great care to provide examples from around the world of negative population growth (today called ). As explained further in , a population which maintains a constant rate of exponential shrinkage is subject to . Hence, the limit to growth problem if a population is subject to a constant rate of negative growth. The problem here is one of extinction!
Modern (17501900) — Freemanpedia
However, I am interested in exponential growth at variable rates. How does itwork in the real world? I have explored this reallife nature of population doubling (and halving) in the article ,which provides a simple model for analysing historical population growthexamples and predicting future population growth.
Agricultural Revolution in England 1500  1850  BBC
I have taken the liberty of using the to quickly extrapolate my results for exponential growth (). Approximate as this method is, the sheer power of exponential growth is revealed. Foran even more powerful example, look at the relative "stability" of thepopulation growing at 1% when compared with that growing at 2%:
The Ottoman Sultans of Turkey & Successors in Romania
I find that population doubling and halving are adequate to explain almost all cases of actual exponential growth. The itself is universal in its application across all time for all .Should you require a greater degree of granularity than is provided through theuse of the (and its reliance on and )then I recommend the use of the .
History of Bluebirds and Bluebirding  Sialis
For the record, whilst I disagree with Cohen's assessment of the exponentialgrowth model (because he ignores Variable Rate exponential growth and negativepopulation growth  see ), I tend to agree with his assessment of the flawed logistic growthmodel. In fact, as I explain below, any set of population growth figuresproduced via a logistic growth model can be derived via the (variable compound interest rates, including negative and positive).
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