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why natural phenomena follow exponential growth?

Discussion in 'Mathematics and Physics' started by PG1995, Aug 29, 2011.

  1. PG1995

    PG1995 Active Member

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    Hi :)


    1: In the context of the definition given below, what does the word "shallower" mean? Here is given the exponential graph.

    2: I have read that many phenomena in nature follow exponential growth. Why is so? Could you please explain how this connection is established between nature and mathematical world? Obviously, if bacterial follows exponential growth, then it is not under any obligation to do so, it does it unknowingly. Besides exponential growth, what other type of growth the natural phenomena most often follow? Please don't use more math to explain math. Thank you.

    Regards
    PG
     
    Last edited: Aug 29, 2011
  2. ARandomOWl

    ARandomOWl New Member

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    Hi

    as opposed to
    ?
     
  3. alec_t

    alec_t Well-Known Member Most Helpful Member

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    It means 'less steep', like a hill which is steep at the base but flattens out towards the top.

    Consider a plant increasing in height at a steady rate of 1cm per week. That is a linear growth rate, with a constant rate of change.

    Consider bacterial replication. Let's suppose it takes 1 second for a bacterium to grow and then divide into two. After 1 sec there will be 2 bacteria. They will also grow and divide, so after 2 secs there will be 4 bacteria. And so on. So the bacterium population, as each second passes, will be 1,2,4,8,16,32,......... which is an exponential population growth rate. This is characterised by a rate of change which is not constant, but instead increases in proportion to the existing population size.
     

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