There's a calculator for this-
https://calculator.academy/population-growth-calculator/
Using this calculator i used the following criteria
initial population of 6, assuming Noah and wife are past child bearing
3% growth rate. World population growth has historically been 2%, i boosted it 50%
Span of 200 years. Check me on this.
Yields 2,200 by the time Nimrod appears Doesnt seem like enough for him to be king over multiple "cities".
For today's population, I'm not smart enough to read the number it spits out.
Of course nobody knows. The numbers can be spun many different ways.