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You really think 21st century demographers, with their longitudinal studies of age cohorts, and billions of dollars riding on government, marketing, and workforce investment, use linear extrapolation from the present? If it were that, things would rather deceptively "look" a good deal better, because the indigenous (white European) population may still be growing a tad in some places, due to the fact that some babies are still being born, while the boomers haven't died off yet.

The problem is the typical 1.2 -1.6 white European fertility rates, when the society's median age edges up past menopause. Historically, no known society has every recovered from that. The number of those not in the workforce based on age or disability inexorably outnumbers new workers coming into the worksforce, which puts increasingly big costs onto the potentially childbearing generation. They bear the burden of provide the upkeep for their elders, and thus they keep delaying and deferring their own childbearing.

The new factors here, are the universal distribution of the means to effectively stop childbirths (contraception, sterilizxationa nd abortion) coupled with a much longer life expectancy (~80) prouducing a huge elderly class plus a childless young adult cohort simultaneously.

This did not happen during the Black Death. This did not happen during the Mongol Invasions. A few years ago Italy became the first nation in history where there are more people over the age of 60 than there are under the age of 20. Germany, Greece and Spain as well as Japan and other Asian Rim nations, have now crossed that same divide.

Don't forget that the potential for childbearing is pretty much limited to about ages 15-35 years old for the females in each age cohort. Fertility declines drastically after that. If you have a situation where the females basically aren't coming anywhere near replacing themselves (think Bologna, Italy, where the fertility rate has been under 1 --- more like 0.8 --- for 20 years), you have a pretty near irreversible problem.

As I said, no known society has ever recovered from this. I didn't do the calculations, anyway. Did you check the links?