But the numbers people here should be able to take a current endgame city and calculate the increase per scout and give us a theoretical number of provinces.
There are two cost increases. The increase for each province scouted, and the increase for going out another ring. Some have suggested that both functions are linear forming a piece-wise function that models a quadratic. If this is the case and the main hall capacity continues to increase in a quadratic form, then in the long run the two should remain fairly proportional, and the scouting time will be the factor that pushes the scouting cost to be a lower percentage of main hall capacity.
However, in order to verify the equation, the rings would need to be factored in, so not all similar size increases in exploration would yield the same increases in cost, as some would cause one to move up a ring while others would not.