Neither counterintuitive nor nonsensical.
Just because it achieves the effect that they want it to have in game does not mean that it is neither counterintuitive nor nonsensical.
Could you imagine being at a meeting for a restaurant chain and then hearing this sentence: "Our number of customers over the past two years has increased nearly sixteen-fold. Consequently, sales are up 400%."
Counterintuitive...and nonsensical (and I realize that my example is not EXACTLY the same thing number-wise, but the difference is actually irrelevant if you think about it).
What I mean is....if you didn't actually LOOK IT UP or ACTUALLY TRACK IT IN GAME, you would think that the taxes would have a linear relation to population. The game itself does not tell you otherwise (at least as far as I know.) That, good sir, is counterintuitive and nonsensical.
Also, thank you for your implied derision, but I am quite good at mathematics, including calculus, although I cannot say that I have a degree in the subject. Anyway, no, I understand how square roots work, and I understand WHY they did it that way. Nevertheless, a non-linear relationship between number of people taxed and taxes yielded is counterintuitive. Anyway, isn't diminishing returns on population already the idea of the approval rating? If they want a logarithmic relation, it should all be there. At least it's not quite as blatantly illogical.