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Doubling time problem

  1. May 7, 2013 #1
    1. The problem statement, all variables and given/known data
    The only functions with a constant doubling time are the exponential functions P0ekt with k > 0. Show that the doubling time of linear function f(t) = a(t) + b at time t0 is t0 + b/a.


    2. Relevant equations
    n/a


    3. The attempt at a solution

    With initial time t0, P = at0 + b

    At some time t, P is doubled: at + b = 2P

    t = (2P - b)/a

    Plug in P and simplify:

    t = (2at0 + b)/a
    t = 2t0 + b/a

    What am I doing wrong?
     
  2. jcsd
  3. May 7, 2013 #2

    Dick

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    Science Advisor
    Homework Helper

    You haven't done anything wrong. But I think they mean the doubling time to be t-t0. That's the length of time after t0 that the function will double. Solve for that.
     
  4. May 7, 2013 #3
    Ahhh, thank you so much.
     
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