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Even withouth the vax there are only 1.6 children per male and female on average
so the 8 billion will drop every 25 years at this ratio
8 billion
6.4 billion
5.2 billion
4 billion
Half the people (4 billion) in 100 years
2 billion in 200 years
1 billion in 300 years
500 million in 400 years
250 million in 500 years
125 million in 600 years
62.5 million in 700 years
31.3 million in 800 years
16 million in 900 years
8 million in 1000 years
4 million in 1100 years
2 million in 1200 years
1 million in 1300 years
500k in 1400 years
250k in 1500 years
125k in 1600 years
12.5k in 2600 years
1.25k in 3600 years
125 in 4600 years
12 in 5600 years
extinct in 6600 years