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I need to work out the amount of time it will take for $X$ to be within $P$% of $C$ using the following formula at $H$ hertz: $$X = X + (C - X)\ Y$$ where $Y$ is a value between $0$ and $1$.

How can I accomplish this?

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I have formatted your question using LaTeX. – Martin Argerami Dec 13 '12 at 13:41
up vote 2 down vote accepted

The first thing to notice is that $X$ always stays at the same side of $C$.

Initially the distance between $X$ and $C$ is $d=|C-X|$. After the first step this distance becomes $(1-Y)d$. After the second step this distance becomes $(1-Y)^2d$. ...

I think this should be sufficient to solve it.

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The third step being $(1-Y)^3d$, right? – Steffan Donal Dec 13 '12 at 13:31
Yes, that is correct. – nvcleemp Dec 13 '12 at 16:34

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