A corollary of this formula is an upper bound of army camp levels. Assuming that the upgrade cost is stored in a 64-bit integer, then the levels of army camps are capped at 75. The actual max level may depend on the level and camp, and I would guess it is capped around 50.
Given that there are so many instances where you get .4 ores per second or .7 money per second, and such, I wouldn't be surprised if most of the values are actually floating-point units. Then, even knowing the bit-size wouldn't tell you much. They can store (almost) arbitrary large numbers. They just get more and more imprecise. But does it really matter whether a 1B upgrade costs 1B or 1B and 1??
I agree that there is probably some upper limit to army camps like there is one for mines. But I wouldn't derive this from a (arbitrary) technical assumption that I personally would want to challenge. In addition, integer are bad at multiplying with fractions like 1.8; another reason why floating-points are more likely.