It's called statistical variance, BTW. Statistically there is no one perfectly fitting geometric curve. There is a fit line that approximates the data though, with individual states falling around it. Some will be a little higher producing a positive error term, some will be a little lower giving a negative error, some will land exactly on the line giving no error. But if the line fits fairly well it will show a geometric trend and predict geometric growth within a plus or minus variation. I don't expect you to comprehend mathematical techniques like that though, and even if you did you're too dishonest to admit it.
Yeah, it's a puzzlement. If you look, for example, at every southern state that participated in the rebellion and not a single one had the rate of growth in free black population between 1850 and 1860 that Illinois had. In spite of the Black codes that you claim should have prevented it, the same kind of black codes that the southern states had. You try to palm it off as a function of population, but Illinois had more free blacks than every one of the original confederate states except Louisiana and South Carolina. By your explanation then those 5 states should have doubled their free black population faster than Illinois. Yet none did, two actually lost black population. You try to explain the growth away as through procreation, but none of the southern states had growth rates near as fast as Illinois. Didn't their free black populations procreate at all? So I'm not sure that you yourself have any concept of statistics or variance or any of that. Illinois would be far to the right on the bell curve. In spite of the laws you claim were there to discourage that population growth.