> TX will arrive at the same point and velocity as NY did, 
> increasing its speed exponentially.

>> 100% agree,  but if you check the speed relationships  during the time,  
>> you will get 2 drastically different numbers regarding acceleration rates,  
>> even with a same endpoint.

Yes, the function predicts the rate of change in the rate of change in speed.  The rate of increase (or decrease) of the acceleration.  In kinetics,  they call this the vector quantity "jerk" or "jolt" - the first time derivative of acceleration, the second time derivative of velocity, and the third time derivative of position.

While calculus is required to really deal with non-linear functions, I presented the far simpler "Rule of 69.3" to estimate the doubling time of infections, deaths whatever.  But with a function (like e^x) one can project the future curve onward from the present one.  

>> I would also postulate that AR did not wear mask, 
>> and FL did  (proportionally of course)  and yet got to the same point!   

But AR had a mask mandate from last July until just recently and FL never had one at all, yet both had similar "per capita" numbers.
So, not only were AR's rates not lower due to the assumed "lower population density", AR had the advantage of masks.

This is twice that AR vs FL has shown us data that is the opposite of what was initially guessed using intuitive factors.  

I'll compound the felony by doing some guessing of my own - I’ll guess that the key difference is larger and multi-generational families in AR, versus the massive number of people living alone or in couples (widowed elderly, young and no kids...)  in FL.  One infection spread to a lot more people "at home" in AR, and thus, spread more quickly.  

One statistic I heard (and cannot verify) is that about 1% of all grandparents alive prior to the outbreak have been lost to the Covid virus.  No idea what normal attrition is for grandparents.

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