If one were to travel to any part of Europe or Asia today one would easily find individuals whose genomes contain about 1 to 4% of genes from Homo neanderthalensis (Green et al. 2010). If you were to ask such an individual how many generations back from the present did your sole Neanderthal relative live to mate with Homo sapiens, then they might put the estimate at 5 to 6 generations or 150 to 180 years (30 years per generation) using the following %DNA formula, understanding that genetic material is halved every generation:

%DNA= 100% x [1/2]^n, where ‘n’ is the number of generations.

Accordingly, after one generation the %DNA from the sole Neanderthal parent would be 50% and after 5 to 6 generations it would be 3.1 to 1.6%. But we all know that Homo neanderthals went extinct 30,000 years ago (Green et al. 2010). Indeed, here we are dealing with populations rather than individuals, and thus it is likely that Neanderthals did not go extinct immediately, but were gradually absorbed by Homo sapiens (the dominant group), an absorption that continues to this very day. From a population point of view, if 30,000 years ago half the population in Eurasia contained Neanderthals and the other half contained Homo sapiens and they intermarried to produce hybrid offspring, then over a 30,000 year period every 5,000 years the genetic contribution of Neanderthals would diminish by 50% (on average) such that by years 5,000 and 0 (today), the percentage of DNA from Neanderthals would, respectively, arrive at 3.1 and 1.6%, approximating current day values.