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## Limits to growth, logistic vs exponential

11 Feb 2016, 19:50 UTC (200 words excerpt, click title or image to see full post)

Malthusian growth modelThe Malthusian growth model sees population growth as exponential.P(t) = PoertwherePo&nbsp;= &nbsp;P(0) is the initial population size,r = population growth ratet = timeGrowth of microbe populations are often used to illustrate this. Let's say an amoeba will grow and divide into two amoeba after an day of absorbing nutrients.Day 1: 1 amoebaDay 2: 2 amoebaDay 3: 4 amoebaDay 4: 8 amoebaAnd so on. Population doubles each day. Exponential growth is famous for starting out slow and then zooming through the roof.On the left is exponential growth in cartesian coordinates. On the right in polar coordinates, radius doubles every circuit.Malthus imagined a rapidly growing population consuming all their available food supply and then starving to death.Logistic growthSometimes populations have suffered Malthusian disaster. More often rate of growth slows as the population approaches the limit that resources can support. This is logistic growth.P(t) = Le-rt&nbsp;/ (L&nbsp;+( e-rt&nbsp;- 1))Where L is the maximum population local resources can support.At the start, logistic growth resembles exponential growth. But as the population nears the logistic ceiling, growth tapers off. Above the blue boundary represents the limit to growth. In red is the logistic growth curve, the thinner black curve is exponential growth.What slows growth?In ...