# Thread: Most efficient method to find this solution-

1. ## 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,

2. 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!

3. Originally Posted by compressedair
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

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

Oh well, thanks a bunch, :]