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Homework Help: Solving for the number of periods in this question

  1. Jul 4, 2015 #1
    1. The problem statement, all variables and given/known data

    I hope everyone is having a great day. The equation I am working with at the moment is:

    (1+ (.2/x))^(x) = 1.21.

    1.21 represents the final value, whereas 1 is the present value. I am trying to solve for x, which represents the number of periods necessary for the entity to grow from 1 to 1.21. I am a little stuck on the algebraic manipulations. If anyone could help that would be awesome, thanks!

    2. Relevant equations

    3. The attempt at a solution

    I have attempted rooting the entire expression, as well as using the "e" and "ln" functions, but I am still having trouble isolating x.
  2. jcsd
  3. Jul 4, 2015 #2


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    There is no proper analytic solution to this type of equation.
    You can get numeric approximations to arbitrary precision.
  4. Jul 4, 2015 #3
    Thank you for clarifying that, as I was pretty confused! Could you tell me where I could find my information on how to do that? Thanks again.
  5. Jul 4, 2015 #4


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    "that" means getting numerical approximations? There are many methods, Wikipedia has a long article as usual. Newton's method is the easiest one that works reasonably well in most cases.

    If you are just interested in a solution for this specific equation, you can guess some numbers, or use WolframAlpha to find solutions. In this case, the integer solution is exact.
  6. Jul 4, 2015 #5


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    Notice that (1.1)2 = 1.21
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