Lake contamination models…

"The time to reach steady state in a perfectly mixed reservoir can be derived from the time that it takes for the term exp[-t/R] go to ≈ zero, which occurs if t = 6R, when 99.75% of Cssp has been reached (600 months in the case of the model lake)." J.C. Varekamp. 2003. Lake contamination models for evolution towards steady state. J. Limnol., 62(Suppl.1): 67-72. The above sentence deserves critical consideration on the grounds of physical and experimental arguments. In an elementary physical system where a capacitor (C farad) is fed a constant electromotive force (volt) with some resistance (R ohm), the electrical charge (q coulomb) varies over time as q = qmax (1-e-t/RC). Using this equation, we can determine the time necessary for the charge to attain some arbitrary fraction of its final value, say 0.9 qmax or 0.999 qmax. This choice is somewhat arbitrary and we must constrain it based on physical considerations.