From the OP link.
This is false or at least misleading. This statistic references "fertility rates", and does not provide any insight into the "exponential function" in a steadily growing population (growth rate).
First, let's consult the "exponential function" which says that the
doubling time of a steady
population growth of 2% = 35 years (1% = 70 yrs)
Thus, only an absolute "zero percent population growth" will result in a stable number and only a negative growth rate will result in a decline in population.
Note that while the projected growth rate has somewhat flattened out @ 11.2 billion, the total population is still increasing, not declining, even as the fertility rate has dropped to 0.1%
But eventually the growth rate must reach zero to avoid a further increase in population and collapsing the earth resources and ecosystem. Any growth rate in excess of zero results in an increase in population. (see Albert Bartlett;
Of course the other option to population control is a good nuclear war wiping out 90 % of mankind, then we could start all over again.