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Calculate exponential growth when rate r is changing

  1. Dec 4, 2012 #1
    The formula f(t) = I(1 + r)t gives the value of something after it has grown for t years, at rate r, with an initial value I.

    What if the growth rate r is continuously increasing?
    What is the formula now?
    Does it relate somehow to xx?
     
  2. jcsd
  3. Dec 4, 2012 #2

    haruspex

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    It depends on how it increases with t. Is it linear with t? Geometric? Logarithmic? ...
     
  4. Dec 5, 2012 #3

    HallsofIvy

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    It is, of course, [itex]f(t)= I(1+ r(t))^t[/itex]. And, yes, that has similar properties to [itex]x^x[/itex], especially if r(t) is linear.
     
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