Changes

** [[Human]] [[population]], if the number of births and deaths per person per year were to remain at current levels

** [[Human]] [[population]], if the number of births and deaths per person per year were to remain at current levels

** Many responses of living beings to stimuli, including [[human]] [[perception]], are [[logarithm]]ic responses, which are the inverse of exponential responses; the loudness and frequency of [[sound]] are perceived logarithmically, even with very faint stimulus, within the limits of perception. This is the reason that exponentially increasing the brightness of visual stimuli is perceived by humans as a linear increase, rather than an exponential increase. This has survival value. Generally it is important for the organisms to respond to stimuli in a wide range of levels, from very low levels, to very high levels, while the accuracy] of the estimation of differences at high levels of stimulus is much less important for survival.

** Many responses of living beings to stimuli, including [[human]] [[perception]], are [[logarithm]]ic responses, which are the inverse of exponential responses; the loudness and frequency of [[sound]] are perceived logarithmically, even with very faint stimulus, within the limits of perception. This is the reason that exponentially increasing the brightness of visual stimuli is perceived by humans as a linear increase, rather than an exponential increase. This has survival value. Generally it is important for the organisms to respond to stimuli in a wide range of levels, from very low levels, to very high levels, while the accuracy] of the estimation of differences at high levels of stimulus is much less important for survival.

*Physics

*[[Physics]]

** Avalanche breakdown within a [[dielectric]] material. A free [[electron]] becomes sufficiently accelerated by an externally applied electrical field that it frees up additional electrons as it collides with [[atom]]s or [[molecule]]s of the dielectric media. These ''secondary'' electrons also are accelerated, creating larger numbers of free electrons. The resulting exponential growth of electrons and ions may rapidly lead to complete [[dielectric breakdown]] of the material.  

** Avalanche breakdown within a [[dielectric]] material. A free [[electron]] becomes sufficiently accelerated by an externally applied electrical field that it frees up additional electrons as it collides with [[atom]]s or [[molecule]]s of the dielectric media. These ''secondary'' electrons also are accelerated, creating larger numbers of free electrons. The resulting exponential growth of electrons and ions may rapidly lead to complete [[dielectric breakdown]] of the material.  

** [[Nuclear chain reaction]] (the concept behind nuclear weapons). Each uranium nucleus that undergoes fission produces multiple [[neutron]]s, each of which can be absorbed by adjacent uranium atoms, causing them to fission in turn. If the [[probability]] of neutron absorption exceeds the probability of neutron escape (a function of the [[shape]] and [[mass]] of the uranium), ''k'' > 0 and so the production rate of neutrons and induced uranium fissions increases exponentially, in an uncontrolled reaction.

** [[Nuclear chain reaction]] (the concept behind nuclear weapons). Each uranium nucleus that undergoes fission produces multiple [[neutron]]s, each of which can be absorbed by adjacent uranium atoms, causing them to fission in turn. If the [[probability]] of neutron absorption exceeds the probability of neutron escape (a function of the [[shape]] and [[mass]] of the uranium), ''k'' > 0 and so the production rate of neutrons and induced uranium fissions increases exponentially, in an uncontrolled reaction.

==External links==

==External links==

*[http://www.webwinder.com/wwhtmbin/jexpont.html Exponent calculator] — One of the best ways to see how exponents work is to simply try different examples.  This calculator enables you to enter an exponent and a base number and see the result.

*[https://www.webwinder.com/wwhtmbin/jexpont.html Exponent calculator] — One of the best ways to see how exponents work is to simply try different examples.  This calculator enables you to enter an exponent and a base number and see the result.

*[http://consumptiongrowth101.com/ExponentialGrowthCalculator.php Exponential Growth Calculator] — This calculator enables you to perform a variety of calculations relating to exponential consumption growth.

*[https://consumptiongrowth101.com/ExponentialGrowthCalculator.php Exponential Growth Calculator] — This calculator enables you to perform a variety of calculations relating to exponential consumption growth.

*[http://www.youtube.com/watch?v=hM1x4RljmnE Understanding Exponential Growth] — video clip 8.5 min

*[https://www.youtube.com/watch?v=hM1x4RljmnE Understanding Exponential Growth] — video clip 8.5 min

*[http://globalpublicmedia.com/dr_albert_bartlett_arithmetic_population_and_energy Dr. Albert Bartlett: Arithmetic, Population and Energy] — sreaming video and audio 58 min

*[https://globalpublicmedia.com/dr_albert_bartlett_arithmetic_population_and_energy Dr. Albert Bartlett: Arithmetic, Population and Energy] — sreaming video and audio 58 min

[[Category: General Reference]]

[[Category: General Reference]]

[[Category: Mathematics]]

[[Category: Mathematics]]