I built up a linear interpolation for Charlotte’s population between 1970 and 1980. In principle, I could extend this beyond those years, and project what the population was before Census Day 1970 or after the census of 1980. Generally, we’d call that — the values the interpolating polynomial takes on, outside the range of data we started with — an extrapolation rather than an interpolation, but they’re pretty closely tied together. If we understand one we’re doing pretty well understanding the other.
[ I cannot and do not try to explain it, but yesterday was a busier-than-average day around these parts, with a surprising number of references coming from an Entertainment weekly article about the House series finale for some reason. In this context a “surprising” number is “any number other than zero” since I don’t know why anyone would go from there to here. I watched House, sometimes, sure, and liked it, but kind of drifted away when there was other stuff to do, you know? ]
That’s enough time spent establishing the heck out of the idea of a polynomial. Let’s actually put one in place. My goal back when was estimating what the population of Charlotte, North Carolina, was around 1975. I had some old Census data from 1970 and 1980 giving its population on the first of April, the earlier year, as 840,347; and the first of April, 1980, as 971,391.