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There are some confounding factors:

- The growth rate is slowing. The growth in absolute terms is still sufficient to make the line look near linear when you look at it over such a long time span, especially given that life expectancy is also increasing almost everywhere (see my last point below).

- The growth rate is fairly low. E.g. around 2005, the growth rate was about 1.1%, and the decline is slow (e.g. it's projected to get to around 0.33% or so around middle of the century), so seeing the change on a graph that plots billions of people against a period of decades gets tricky.

- There are large temporal distortions due to changes in life expectancy, and the size of generations. To give an extreme example: Consider if a population to begin with was static - births and deaths were perfectly matched. Now consider if this population stopped having children, yet at the same time, everyone started living 40 years longer. In this (totally impossible of course) scenario, it would take 40 years from the birthrate collapsed until the population size would start dropping. While something that extremely obviously would not happen, less extreme variations are. E.g. some areas of China has a birth rate of well below 1 child per woman, and the country as a whole is well below 2, while you need somewat more than 2 to maintain a population (to account for men + people who never procreate), but the population is still increasing because population is still young on average due to the massive population growth in the 50's and 60's coupled with rapidly increasing life expectancy.

This last point means that we're still seeing a combination of the effect of birth rates going as far back as at least 1950's and all increases in life expectancy since, that correctly reflects current growth, but gives us a very distorted idea of where the population size is headed.




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