Not necessarily so. Theoretically, it under 100 years, China's population should be halved, due to their 1 child p/family rule. Of course, 'elixirs' not withstanding.
Even just such factors as a high cost of living makes wanting more children a thing of the past, as is evidence throughout many parts of the world.
If we can just get enough condoms over to the third world countries, and teach them to use the darn thingys, there's still hope that the population in 100 years would still be manageable. IMO
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