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Math Help - Most efficient method to find this solution-

  1. #1
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    Most efficient method to find this solution-

    I've been trying to think of a better solution for this problem, so far it looks like I'm stuck running an arbitrarily long brute-force loop (or having to keep track of various 'statistics' on the variables over time, which doesn't help me much in a few cases), which I'm trying to find a way around.

    These are the three key variables as initiated by a program;
    A = 0.985, B = 0.0018, and C = 0.

    For each moment in time I will perform the two following calculations:
    C = C * A;
    C = C + B;

    The question is 'what value will C be where the decrement of A will cancel out the increment of B.'

    For example, the solution to the above is: 0.1199999967, which occurs on the 1,142 iteration.
    (0.1199999967 * 0.985) + 0.0018 = 0.1199999967

    I want to find the point where C will stop increasing without having to employ brute-force.

    Thanks,
    Last edited by compressedair; October 31st 2009 at 03:24 PM. Reason: Simplifying the question since an answer has been given.
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  2. #2
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    Just a quick thought, maybe deciding on a limit for C ahead of time and how many iterations I would like for C to work through before reaching said limit, then derive A and B from that? Probably not easier... hrm. Lol, arrrgggh!
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  3. #3
    Grand Panjandrum
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    Quote Originally Posted by compressedair View Post
    Just a quick thought, maybe deciding on C ahead of time and how many iterations I would like for C to work through before reaching its limit, then derive A and B from that? Probably not easier... hrm. Lol, arrrgggh!
    The final limiting value of C if it exists is:

    C=\frac{B}{1-A}

    CB
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  4. #4
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    Damn, can't believe I couldn't realize it should have been 1-A, ... well that's annoying. :\

    Oh well, thanks a bunch, :]
    Last edited by compressedair; October 31st 2009 at 03:30 PM. Reason: m --> r
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