I realize the original post wants to do this in GIS, so if you already know how to do this outside of GIS, skip this comment. This is a regression problem, where your x variable varies over time (x in the graph). You can simply plot the points (in Excel, R, or whatever) and calculate the regression line to extrapolate outside the measured range. Find the equation for the regression line, and solve for your x. For example, in the attached graph, I made up y values: 1984 = 0, 1986 = 1, 1992 = 4.5, 1999 = 4.6, 2003 = 6, 2004 = 6.1, 2010 = 6.8 (obviously you have the correct x values). 2014 would have a value of 8.521.