25% twice per week creates greater stability...but one 50% water change removes more waste.
If x0 = the initial amount of waste (nitrate) in the tank (mg) and
z= the amount of waste (nitrate) produced per day (mg/day) - assuming constant waste production, and
x7 @ 50% = the amount of waste (nitrate) in the tank after one week in mg
x7 @ 50% = x0 + 7z - .5x0 - .5*7*z
x7 @ 50% = .5x0 + 3.5z
For two 25% water changes per week (on day 3 and day 7):
x3 @ 25% = the amount of waste in the tank (nitrate, mg) after 25% water change on day 3
x3,7 @ 25% = the amount of waste in the tank (nitrate, mg) after 25% waste change on day 7
x3 @ 25% = x0 + 3z - .25x0 - 3*.25z
x3 @ 25% = x0 + 2.25z
x3,7 @ 25% = x3 @ 25% + 4z - .25 * x3 @ 25% - 4 * .25z
x3,7 @ 25% = .5625x0 + 4.6875z
Which is larger (x7 @ 50% or x3,7 @ 25%)?
Assuming x0 = 0, at any rate of waste (nitrate) production, x 3,7 @ 25% is going to have more waste (nitrate) on day 7.
Maybe my math's messed up but makes sense to me
Matt
If x0 = the initial amount of waste (nitrate) in the tank (mg) and
z= the amount of waste (nitrate) produced per day (mg/day) - assuming constant waste production, and
x7 @ 50% = the amount of waste (nitrate) in the tank after one week in mg
x7 @ 50% = x0 + 7z - .5x0 - .5*7*z
x7 @ 50% = .5x0 + 3.5z
For two 25% water changes per week (on day 3 and day 7):
x3 @ 25% = the amount of waste in the tank (nitrate, mg) after 25% water change on day 3
x3,7 @ 25% = the amount of waste in the tank (nitrate, mg) after 25% waste change on day 7
x3 @ 25% = x0 + 3z - .25x0 - 3*.25z
x3 @ 25% = x0 + 2.25z
x3,7 @ 25% = x3 @ 25% + 4z - .25 * x3 @ 25% - 4 * .25z
x3,7 @ 25% = .5625x0 + 4.6875z
Which is larger (x7 @ 50% or x3,7 @ 25%)?
Assuming x0 = 0, at any rate of waste (nitrate) production, x 3,7 @ 25% is going to have more waste (nitrate) on day 7.
Maybe my math's messed up but makes sense to me
Matt