1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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?

  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


    User Avatar
    Science Advisor
    Gold Member

    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


    User Avatar
    Science Advisor

    Another (identical) way to define exponential growth is a growth rate proportional to the current value. The classic example is population.
    #dp/dt = rp#
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook