These aren't even the beginning of the factors involved in child birth rates. Population is controlled by religion, government policy, cultural practice, wealth, quality of life, social equality, education, trade, war, climate, and a host of other factors. Any one of them could change and affect the population; multiple could change and shift it radically. And we cannot predict any of them with certainty even in 50 years, much less 100, for the entire planet.

If you don't believe me, look at history. Plenty of times in history there have been great civilizations that grew and grew until they collapsed, or periods of great societal progress followed by periods of great strife, or periods of great feast followed by famine. Some of these periods lasted hundreds of years. Even today there are nations that forcibly control population whereas others do not. Some developing nations starve due to international trade policy while others grow to provide most of their needs. Some become more radically conservative while others grow more liberal. Some countries collapse economically while others become burgeoning super-powers. And all this in the face of global climate change on a scale not seen in millennia.