USDA in Missouri has been the driving force for the use of this equation here. It is called out as coming from the Missouri Division of Health (original DNR). It was presented in a Health Department circular circa 1966 as 12*n^0.515; but, data seen by USDA shows this to be a bit excessive.
I have a printing of an article (provided by USDA) from "Water and Sewage Works, July 1951" written by D.R. Taylor, General Manager that provided a table of water use based on the number of houses and class of houses. These values were obtained through metered users over several years of testing. This table, when plotted, graphs the Class 3 home (Avg good subdivision with 80% two to 3 bedroom houses with 1 bath and 20% two to 3 bedroom houses with 2 baths. Houses owned by occupant, with average amount of lawn and shrubbery requiring average amount of lawn sprinkling) at the 9*n^0.515.
I don't know if this information is printed elsewhere; but, from experience, it is working on our systems. I've had system owners come to us (after extending lines to pick up additional users) with pressure/volume problems and this equation, when used, shows the problem to be real similar to what is found in the field.