Yes, this gets to me too. You can fit any sequence of n points with a curve described by a polynomial of n-1 degree. therefore, you need at least 4 points to k

Yes, this gets to me too. You can fit any sequence of n points with a curve described by a polynomial of n-1 degree. therefore, you need at least 4 points to know that the curve is not cubic, and an infinite number to know that it is exponential (though you can usually surmise as much sooner, because many natural phenomena are exponential or logarithmic).