Note that the occupancy of the RR site increases now with the square of R's concentration. This makes it more like a switch. The problem is not quite over. We really should consider the fact that while R's concentration may be much larger than O's concentration (there is typically only one O per cell), it may not be much larger than RR's concentration. Since what we usually know is RTot, we should solve for R in terms of RTot:

This value for R can be used in the previous equation for a more accurate result.