In mathematics, exponential growth (or geometric growth) occurs when
the growth rate of a function is always proportional to the function's
current size. Such growth is said to follow an exponential law (but
see also Malthusian growth model). This implies for any exponentially
growing quantity, the larger the quantity gets, the faster it grows.
But it also implies that the relationship between the size of the
dependent variable and its rate of growth is governed by a strict law,
of the simplest kind: direct proportion...
...As discussed above, an important point about exponential growth is
that even when it seems slow on the short run, it becomes impressively
fast on the long run, with the initial quantity doubling at the
doubling time, then doubling again and again. For instance, a
population growth rate of 2%% per year may seem small, but it actually
implies doubling after 35 years, doubling again after another 35 years
(i.e. becoming 4 times the initial population), etc. This implies that
both the observed quantity and its time derivative will become several
orders of magnitude larger than what was initially meant by the person
who conceived the growth model. Because of this, some effects not
initially taken into account will distort the growth law, usually
moderating it as for instance in the logistic law. Exponential growth
of a quantity placed in the real world (i.e. not in the abstract world
of mathematics) is a model valid for a temporary period of time only.
For this reason, some people challenge the exponential growth model on
the ground that it is valid for the short term only, i.e. nothing can
grow indefinitely. For instance, a population in a closed environment
cannot continue growing if it eats up all the available food and
resources; industry cannot continue pumping carbon from the
underground into the atmosphere beyond the limits connected with oil
reservoirs and the consequences of climate change; etc. Problems of
this kind exist for every mathematical representation of the real
world, but are specially felt for exponential growth, since with this
model growth accelerates as variables increase in a positive feedback,
to a point were human response time to inconvenients can be
insufficient (on these points, see also the Exponential stories
below)...
http://en.wikipedia.org/wiki/Exponential_growth
A quantity is said to be subject to exponential decay if it decreases
at a rate proportional to its value.
http://en.wikipedia.org/wiki/Exponential_decay
---------------
-- If, as with some birds; population regulation in our study
species, is regulated not by one but by multiple negative feedback
mechanisms, drought freezes hurricane floods forest fires, ...here,
then, was a dramatic example of how competition among members of one
species for a finite resource - in this case, food - caused a sharp
drop in population. [trying to find the study where the places where
they breed limits the number of offspring, Then humans, through
proggressive problems will emulate these constraints, attend to
reproductive rates, and make a bold move as they have tried to do in
China, and have "good reason" which will forcefully persuade people to
choose reproductive controls, but we are still coming out of an
environment where attention to reproduction has been a much lower
priority than it will be as problems increase, consequently, we might
consider many examples of where something was regulated because of
immediate concerns, kind of like economic thinking and supply and
demand, hence we either reproduce and take up everything and go
extinct, or manage our population growth, wherein we adjust our laws
accourding to a network of constraints. But thats what your probably
meaning but that you want all this to happen slower of faster? --
Reanimater
--------------------
The effect was clearly density-dependent. The lower population
densities of the previous summer had permitted most of the animals to
complete their life cycle...
...These results, combined with demographic modeling, suggest that the
negative feedback found in long term demographic data is strong enough
to regulate the local population at the densities observed (Sillett &
Holmes in press), and may be generated by one or more regulatory
mechanisms, either acting singly or together (Rodenhouse et al. 1999).
To date, therefore, the results from long-term demographic monitoring,
the density reduction experiment, site suitability measures, and
demographic models suggest that population regulation in our study
species, and probably other songbirds, is regulated not by one but by
multiple negative feedback mechanisms.
http://users.rcn.com/jkimball.ma.ultranet/BiologyPages/P/Populations2.html
I just finished the book Consilience, by E.O. Wilson, the thrid time
and he mentioned that, if you stacked the billion of bodies on earth
like logs in a woodpile that all of us would fit in one corner of the
Grand Canyon.
http://en.wikipedia.org/wiki/Consilience
http://www.2think.org/hii/wilson.shtml
http://www.amazon.com/Consilience-Knowledge-Edward-O-Wilson/dp/0679450777
In mathematics, exponential growth (or geometric growth) occurs when
the growth rate of a function is always proportional to the function's
current size. Such growth is said to follow an exponential law (but
see also Malthusian growth model). This implies for any exponentially
growing quantity, the larger the quantity gets, the faster it grows.
But it also implies that the relationship between the size of the
dependent variable and its rate of growth is governed by a strict law,
of the simplest kind: direct proportion...
...As discussed above, an important point about exponential growth is
that even when it seems slow on the short run, it becomes impressively
fast on the long run, with the initial quantity doubling at the
doubling time, then doubling again and again. For instance, a
population growth rate of 2%% per year may seem small, but it actually
implies doubling after 35 years, doubling again after another 35 years
(i.e. becoming 4 times the initial population), etc. This implies that
both the observed quantity and its time derivative will become several
orders of magnitude larger than what was initially meant by the person
who conceived the growth model. Because of this, some effects not
initially taken into account will distort the growth law, usually
moderating it as for instance in the logistic law. Exponential growth
of a quantity placed in the real world (i.e. not in the abstract world
of mathematics) is a model valid for a temporary period of time only.
For this reason, some people challenge the exponential growth model on
the ground that it is valid for the short term only, i.e. nothing can
grow indefinitely. For instance, a population in a closed environment
cannot continue growing if it eats up all the available food and
resources; industry cannot continue pumping carbon from the
underground into the atmosphere beyond the limits connected with oil
reservoirs and the consequences of climate change; etc. Problems of
this kind exist for every mathematical representation of the real
world, but are specially felt for exponential growth, since with this
model growth accelerates as variables increase in a positive feedback,
to a point were human response time to inconvenients can be
insufficient (on these points, see also the Exponential stories
below)...
http://en.wikipedia.org/wiki/Exponential_growth
A quantity is said to be subject to exponential decay if it decreases
at a rate proportional to its value.
http://en.wikipedia.org/wiki/Exponential_decay
---------------
-- If, as with some birds; population regulation in our study
species, is regulated not by one but by multiple negative feedback
mechanisms, drought freezes hurricane floods forest fires, ...here,
then, was a dramatic example of how competition among members of one
species for a finite resource - in this case, food - caused a sharp
drop in population. [trying to find the study where the places where
they breed limits the number of offspring, Then humans, through
proggressive problems will emulate these constraints, attend to
reproductive rates, and make a bold move as they have tried to do in
China, and have "good reason" which will forcefully persuade people to
choose reproductive controls, but we are still coming out of an
environment where attention to reproduction has been a much lower
priority than it will be as problems increase, consequently, we might
consider many examples of where something was regulated because of
immediate concerns, kind of like economic thinking and supply and
demand, hence we either reproduce and take up everything and go
extinct, or manage our population growth, wherein we adjust our laws
accourding to a network of constraints. But thats what your probably
meaning but that you want all this to happen slower of faster? --
Reanimater
--------------------
The effect was clearly density-dependent. The lower population
densities of the previous summer had permitted most of the animals to
complete their life cycle...
...These results, combined with demographic modeling, suggest that the
negative feedback found in long term demographic data is strong enough
to regulate the local population at the densities observed (Sillett &
Holmes in press), and may be generated by one or more regulatory
mechanisms, either acting singly or together (Rodenhouse et al. 1999).
To date, therefore, the results from long-term demographic monitoring,
the density reduction experiment, site suitability measures, and
demographic models suggest that population regulation in our study
species, and probably other songbirds, is regulated not by one but by
multiple negative feedback mechanisms.
http://users.rcn.com/jkimball.ma.ultranet/BiologyPages/P/Populations2.html
