The Malthusian growth model, sometimes called the simple exponential growth model, is essentially exponential growth based on a constant rate of compound interest. The model is named after the Reverend Thomas Malthus, who authored An Essay on the Principle of Population, one of the earliest and most influential books on population. In mathematics, a quantity that grows exponentially is one whose growth rate is always proportional to its current size. ... Compound interest, is interest which is added to the original principal. ... The Rev. ... An Essay on the Principle of Population was first published anonymously in 1798. ...

Exponential law

As noted by doctor Peter Turchin (Does population ecology have general laws?, 2001 and Complex Population Dynamics, 2003), this model is often referred to as The Exponential Law and is widely regarded in the field of population ecology as the first principle of population dynamics, with Malthus as the founder. Peter Turchin, is a world known specialist in population dynamics and mathematical modeling of historical dynamics. ... Population ecology is a major subfield of ecology—one that deals with the dynamics of species populations and how these populations interact with the environment. ... In a formal logical system, that is, a set of propositions that are consistent with one another, it is probable that some of the statements can be deduced from one another. ... Population dynamics is the study of marginal and long-term changes in the numbers, individual weights and age composition of individuals in one or several populations, and biological and environmental processes influencing those changes. ... The Rev. ...

At best, it can be described as an approximate physical law as it is generally acknowledged that nothing can grow at a constant rate indefinitely (Cassell's Laws Of Nature, Professor James Trefil, 2002 - Refer 'exponential growth law'). Professor of Populations Joel E. Cohen has stated that the simplicity of the model makes it useful for very short-term predictions and of not much use for predictions beyond 10 or 20 years (How Many People Can The Earth Support, 1995). Philosopher Antony Flew - in his introduction to the Penguin Books publication of Malthus' essay (1st edition) - argued a "certain limited resemblance" between Malthus' law of population to laws of Newtonian mechanics. This view has been echoed by many other philosophers since. Also, "e: The Story Of A Number" by Eli Maor (1994) , "What Evolution Is" by Ernst Mayr, (2001) ,"The Complete Idiot's Guide To Calculus" by W. Michael Kelly (2002) and "The Galilean turn in population ecology" Mark Colyvan and Lev R. Ginzburg (2003). A physical law, scientific law, or a law of nature is a scientific generalization based on empirical observations of physical behavior. ... James S. Trefil (b. ... Antony Flew. ... Penguin Books is a British publisher founded in 1935 by Allen Lane. ... It has been suggested that this article or section be merged with Classical mechanics. ... This article has been identified as possibly containing errors. ...

Malthusian law

The exponential law is also sometimes referred to as The Malthusian Law (refer "Laws Of Population Ecology" by Dr. Paul Haemig, 2005).

Rule of 70

The Rule of 70 is a useful rule of thumb that roughly explains the time periods involved in exponential growth at a constant rate. For example, if growth is measured annually then a 1% growth rate results in a doubling every 70 years. At 2% doubling occurs every 35 years. The Rule of 70 is a financial term derived to determine the time it takes for the value of money to halve due to a given inflation rate. ... A rule of thumb is an easily learned and easily applied procedure for approximately calculating or recalling some value, or for making some determination. ... In mathematics, a quantity that grows exponentially is one whose growth rate is always proportional to its current size. ...

Logistic growth model

The Malthusian growth model is the direct ancestor of the logistic function. Pierre Francois Verhulst first published his logistic growth function in 1838 after he had read Malthus' An Essay on the Principle of Population. Benjamin Gompertz also published work developing the Malthusian growth model further. Logistic curve, specifically the sigmoid function A logistic function or logistic curve models the S-curve of growth of some set P. The initial stage of growth is approximately exponential; then, as competition arises, the growth slows, and at maturity, growth stops. ... Pierre François Verhulst (October 28, 1804 - February 15, 1849, Brussels, Belgium) doctor in number theory from the University of Ghent 1825. ... An Essay on the Principle of Population was first published anonymously in 1798. ... Benjamin Gompertz (March 5. ...

See also

• Albert Bartlett - a leading proponent of the Malthusian Growth Model
• Bacterial growth - Bacteria are often cited as growing exponentially
• Cell growth - Cells are sometimes cited as growing exponentially
• Exogenous growth model - related growth model from economics
• Fibonacci number - A related idea from Leonardo of Pisa or Leonardo Pisano (Pisa, c. 1170 - Pisa, 1250), also known as Fibonacci
• Growth theory - related ideas from economics
• Population
• Mathematical models
• Molecular Nanotechnology - K. Eric Drexler's Assemblers are anticipated to be able to grow via exponential assembly. Some are worried about the grey goo catastrophe.
• Neo-malthusianism
• Logistic function
• Scientific laws named after people - strictly speaking, no scientific law has been named after Malthus
• Scientific phenomena named after people - being mathematical, and relating to population dynamics, the Malthusian Growth Model qualifies

Albert A. Bartlett is a retired Emeritus Professor of Physics University of Colorado, Boulder, USA. Professor Bartlett has lectured over 1,500 times on Arithmetic, Population, and Energy. He has famously stated that The greatest shortcoming of the human race is our inability to understand the exponential function. ... Bacterial growth is process in which two clone daughter cells are produced by the cell division of one bacterium. ... The term cell growth is used in two different ways in biology. ... The Exogenous growth model, also known as the Neo-classical model or Solow growth model is a term used to sum up the contributions of various authors to a model of long-run economic growth within the framework of neoclassical economics. ... This article or section does not cite its references or sources. ... A tiling with squares whose sides are successive Fibonacci numbers in length A Fibonacci spiral In mathematics, the Fibonacci numbers form a sequence defined by the following recurrence relation: That is, after two starting values,each number is the sum of the two preceding numbers. ... Leonardo of Pizza (1170s or 1180s – 1250), also known as Leonardo Pisano, Leonardo Bonacci, Leonardo Fibonacci, or, most commonly, simply Fibonacci, was an Italian mathematician, considered by some the most talented mathematician of the Middle Ages. ... Economic growth is the increase in the value of goods and services produced by an economy. ... This article or section does not cite its references or sources. ... Note: The term model is also given a formal meaning in model theory, a part of axiomatic set theory. ... It has been suggested that Molecular engineering be merged into this article or section. ... Kim Eric Drexler (born April 25, 1955) is an American engineer best known for popularizing the potential of hypothetical molecular nanotechnology. ... This article is about a computing term. ... Exponential assembly is a theoretical nanofactory process patented by Zyvex. ... Grey goo refers to a hypothetical end-of-the-world scenario involving molecular nanotechnology in which out-of-control self-replicating robots, deliberately designed and built in a way known to be dangerous, consume all living matter on Earth while building more of themselves (a scenario known as ecophagy). ... Neo-malthusianism is a set of doctrines which have their precedent with Thomas Malthuss concept of limited resources keep populations in check and reduce economic growth. ... Logistic curve, specifically the sigmoid function A logistic function or logistic curve models the S-curve of growth of some set P. The initial stage of growth is approximately exponential; then, as competition arises, the growth slows, and at maturity, growth stops. ... This is a list of scientific laws named after people (eponymous laws). ... The Rev. ... This is a list of scientific phenomena and concepts named after people (eponymous phenomena). ... Population dynamics is the study of marginal and long-term changes in the numbers, individual weights and age composition of individuals in one or several populations, and biological and environmental processes influencing those changes. ...

External links

• Malthusian Growth Model from Steve McKelvey, Department of Mathematics, Saint Olaf College, Northfield, Minnesota
• Logistic Model from Steve McKelvey, Department of Mathematics, Saint Olaf College, Northfield, Minnesota
• Laws Of Population Ecology Dr. Paul D. Haemig
• On princples, laws and theory of population ecology Professor of Entomology, Alan Berryman, Washington State University
• Mathematical Growth Models
• e the EXPONENTIAL - the Magic Number of GROWTH - Keith Tognetti, University of Wollongong, NSW, Australia
• Professor Peter Turchin's web page
• Introduction to Social Macrodynamics Professor Andrey Korotayev
• Professor Joel E. Cohen's web page
• Interesting Facts about Population Growth Mathematical Models from Jacobo Bulaevsky, Arcytech.