The next number in the series is always 19.
Given any finite list of x and y values, there are an infinite number of functions that those y values exactly at each of the x values. At any x value not given in the list, there are then an infinite number of possibilities for y, and there is no "correct" way of determining what the corresponding y "really" is.
Therefore one might as well pick any arbitrary number as being the "real" next number in the sequence.
Consider that, after all,
polyfit([0 10 20 30 40 50 60 70 80 90], [78.54 76.19 73.65 70.85 67.72 64.26 60.19 19 19 19], 9)
should be able to come up with a perfect fit, to within the limits of floating point accuracy. Any sequence extended by any arbitrary value can still mathematically be fit by some function.
polyfit([0 10 20 30 40 50 60 70 80 90], [78.54 76.19 73.65 70.85 67.72 64.26 60.19 42 42 42], 9)
should also be able to come up with a perfect fit to within floating point accuracy
So generate any value you like and you will be right.
