I'm just a neuroscientist, so forgive me if the answer to this question is either obvious, or the answer is that it is impossible, obviously.(adsbygoogle = window.adsbygoogle || []).push({});

Basically, this image should outline the question clearly

http://img713.imageshack.us/img713/2569/mathsissuefixedyxs.gif [Broken]

(And Y0 is always 1)

Also, I tried just fitting an exponential to the output. For instance, if I set Y0=1, i = 1, k = 1 and D=0.5, then the output is explained by the curve Yn = (1 - 0.7746)*e^(1.693 * t) + 0.7746 so I can't see the relation, between the fit constants constants in the numerical method

Oh, and just in case anyone is confused about the exponential recovery process equation

yn = (y(n-1) * D) + (1 - y(n-1) * D) * (1 - e^(-k*i))

I modeled it after the general equation for exponential recovery

Y = initial value + (asymptote - initial value) * (1 - e^(-k*x))

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# Converting a problem solved with numerical analysis to a simple exponential

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