Ah I see. I thought you were referring also to the CO2 related drop in pH when you posted that. Anyway, is there a source to read about the relationship if it's too complicated to explain on the forum? As long as it doesn't go beyond partial differential equations or transformations of any sort, I should be able to follow.
I am not sure of actual mathematical equations relating these parameters to pH, all I know is what I stated in the post, that certain parameters either have a positive or negative relationship with each other. Not sure what kind, such as direct, quadratic, etc. that could get very complicated, too complicated to bother with. But what I was saying, about the derivatives, if what hoppy was saying is correct, then that means that change in pH (Y) is a function of change in KH (X) (X change in KH results in Y change in pH). This means that the derivative of this function (dy/dx) is independent of CO2. This does not mean that the variable of pH (Y) itself is independent of CO2. If it was, then (dy/dz) would be zero, meaning that CO2 would not affect pH. So, pH has some sort of relationship with CO2 (Z) a very complex one. pH (Y) is dependent on both pH and CO2, but dy/dx and dz/dy are independent of each other.
Ok, hold on, based on what hoppy said, the equation is Z/Zo=10^(Yo-Y) which means Z=Zo[10^(Yo-Y)]
so to calculate CO2(Z), you plug in starting ph for Yo, and current pH for Y and I guess we are assuming that the starting CO2 is 3ppm? That would have to be true for the equation. Is that true Hoppy? is that for aquarium water?
Wow that was a doozy, im gonna forget about math for a few days now...