Logarithms in Nature
Why does nature follow logarithm pattern?
Logorithms are exponential functions in reverse. Exponential functions are
based on a very simple relationship: rate of growth is proportional to
current size. If the rate at which something increases is proportional to
how big it is, you have an exponential ralationship. A common example of
this is population. The rate of growth of a population of flowers from year
to year is proportional to the number of seeds produced. Twice as many
flowers will produce twice as many seeds. If in no way limited by available
ground, weather, or insects, number of flowers will increase exponentially.
Logorithms come into play in two different circumstances. One is when you
need to discover how much time is required for a cartain number of flowers
to exist. Using time to discover population is exponential. Using
population to discover time is logorithmic. Another use for logorithms is
when rate of growth is inversely proportional to number. One example has to
do with food limitation. Assume there is the ideal amount of food for a
certain population of bears. If the population were doubled, each bear only
gets about half as much food. Only about half as many bear cubs survive.
If no adult bears die, the population will grow logorithmically.
Many quantities in nature have such relations. Many quantities in nature
vary exponentially or logorithmically.
Dr. Ken Mellendorf
Illinos Central College
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Update: June 2012