How Long Would It Take To Solve a 100x100 Cube?

Your approximation is way too large because your best fit polynomial was quartic and you should have used a quadratic

If you use a quadratic polynomial on the even NxNxN records then you get an estimate of around 50 hours, and if you use all NxNxN records from 4 to 15 then you get around 57.5 hours, and the times for an NxNxN cube being roughly 20N^2 or 23N^2. This seems much more reasonable compared to the actual 100x100 record
 
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quadratic also makes sense because you expect difficulty to scale with cubies visible which scales quadratically
 
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