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Math Help - From A to B, exponentially

  1. #1
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    From A to B, exponentially

    moderators if this isn't the appropriate sub forum please redirect the post, thanks)
    Hello friends

    Say I have two values A and B; I also have a given number of days (or "steps"), nominated Z. to reach from A to B by any mathematical operation. if I wanted to do it linearly the equation would be
    (A-B)/Z would give me the subtraction element I must subtract from A every day to reach B in Z days.
    let
    A = 1.6
    B = 1
    Z = 25 (these are my actual numbers I need to calculate btw)
    so (1.6-1)/25 = 0.024 is my answer.

    BUT what if I need to get to value B exponentially, so that the rate of change is increasing with every day passing? how do I solve that?

    thanks!
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  2. #2
    MHF Contributor ebaines's Avatar
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    Re: From A to B, exponentially

    You can use:

     R = (\frac B A)^{1/Z}

    Then for each step you multiply the previous step by R. For example; if A = 3 and B = 7, and you want to get from A to B in four steps (Z=4) this equation yields:

     R = (\frac 7 3 })^{1/4} = 1.236

    and the steps are;

    3,
    3 x 1.236 = 3.708,
    3.708 x 1.236 = 4.582,
    4.582 x 1.236 = 5.664,
    5.664 x 1.236 = 7
    Thanks from topsquark
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