Originally Posted by Mikaila31
That equation isn't an accurate calc of the effects of a water change on parameters. It may seem straightforward but its not. Also it is a recursive calculation meaning the answer feeds back into it repetitively, which is they key to the leveling off.
a(n) = [a(n-1) + w][1-x] + xz, n>=1, a(0)=y
y=starting nitrate in tank b4 1st wc, z=tap parameters, w=buildup of nitrate b4 each wc, x= % wc in decimal, n= # of wc's
You equation is after the water change.
parameters before water change=amount in replacement water+(increase)/(fraction of water change)
Is before the water change and after sufficient water changes have been performed so the amount before water change is the same water change to water change. In other words where the tank winds up.
I have found out that by looking at the amount before the water change simplifies the equation considerably and allows a better analysis. for instance if you "tie" the amount of water change to the frequencey (1/10 every 10 days, 1/20 every 20 days, etc), the amount before the water change winds being the same. The amount after the water change varies with the amount/frequency.
The reason this works is that in order for the final conditions to be met, the amount removed by the water change must be removed by the water change. So if you're doing a 1/10 water change, the parameters must be 10 times the build up, 1/5 5 times, 1/100 100 times and so on.
I have already plotted the equation and found that the values reach that limit in a very short while. Like say 5% within a few months or so.
Check your charts and you will find that to be true.
Again in case anyone missed it. Fw and marine systems unmeasureable ammonia,nitrItes, nitrate, and phospahtes. PH 8.4-8.8. Calcium/alk/mag have to be maintained with dosing in reef tanks. FW tanks with peat moss in the substrate kh 4 degrees, gh 9 degrees for over two years. kh and gh do rise over years in FW tank with a plain sand substrate and neon tetras do not do well.