Given a set of data pairs, how would you decide whether to use interpolation or extrapolation to find a certain value?

Answer 1

use interpolation when the data falls within the range given by the model (when it says "based on data from such and such to such and such" or "this data applies to years x to y" when the year or time you're studying falls outside this range then you are using extrapolation

Answer 2

also, if you have a chart the x values in the chart represent the data range used for interpolation while anything lower than the min x value will be extrapolation and any term higher than the max x value will be extrapolation.