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What does exponential growth really mean?

  1. Jul 11, 2015 #1
    I've always thought that when people say exponential growth, they mean [itex]e^x[/itex].

    But other times I hear people just say that the quantity doubles [itex]2^x[/itex] every time.

    So which is it? And if it's just doubling, why don't we say that [itex]3^x[/itex] or [itex]4^x[/itex] is exponential growth as well, since that's what those functions are technically called?

    Thanks
     
  2. jcsd
  3. Jul 11, 2015 #2
    Any number raised to a positive variable power is exponential growth. The rules of logs and exponents can be used to convert one equation A^x to any other equivalent aB^x.

    Exponential growth means the rate of growth of a quantity is proportional to the amount currently present.
     
  4. Jul 11, 2015 #3

    DrGreg

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    Exponential growth means [itex]e^{kx}[/itex] for any constant [itex]k[/itex]. But[tex]
    a^x = e^{x \log_e a}
    [/tex]so [itex]a^x[/itex] is also exponential growth for any constant [itex]a[/itex].
     
  5. Jul 11, 2015 #4
    Another (identical) way to define exponential growth is a growth rate proportional to the current value. The classic example is population.
    #dp/dt = rp#
     
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