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Proving the constant rate of doubling for an exponential function

  1. Sep 11, 2007 #1
    1. The problem statement, all variables and given/known data
    Given that Q=Pa^t and Q doubles between t and t+d, prove that d is the same for all t.


    2. Relevant equations

    Q=pa^t

    3. The attempt at a solution

    This is what I've tried so far:

    [tex]Q_0=Pa^t[/tex] and [tex]Q_1=Pa^{t+d}[/tex]
    Then:
    [tex]\frac{a^{t+d}}{a^t}} \equiv 2[/tex]

    This is where I begin drawing blanks again. I want to say take the log, but I'm not sure if that is right.

    If so, doesn't this give me:
    [tex]\frac{t+d}{t} \equiv log(2)[/tex] ?

    Then from there: [tex]d \equiv log(2^t)-t[/tex]

    Would that be correct?
     
  2. jcsd
  3. Sep 12, 2007 #2

    NateTG

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    Science Advisor
    Homework Helper

    Hint:
    [tex]Q^{t+d}=Q^t+Q^d[/tex]

    Alternatively:
    [tex]\log \frac{a}{b}= \log a - \log b[/tex]
     
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