Volitional/conscious beings that live with integrated honesty will always solve the problems that thwart their immortality. They would never initiate force, fraud or coercion against any person and certainly not forced nonfertility.
Every volitional/conscious being living with integrated honesty is a huge benefit to civilization and produces more values than he or she consumes. Furthermore, when living forever is really forever each person will eventually create/produce more values than all values combined that were present at their time of birth.
Now we have 6 billion. Lets let 18 years (another fudge factor) pass for those to mature and assume we now have 3 billion women. Each one bears a child.
Now we have 9 billion. 18 years. 4.5 billion women, each one bears a child.
13.5 billion, lets add another fudge and round off to 13. 18 years. 18 years. 6.5 billion women, each one has a child.
Now we have 19.5, round off to 19. 18 years. 9.5 biooion women, each bears a child.
Now we have 28.5 billion, round to 28. 18 years. 14 billion women, each bears child.
32 billion. 18 years. 16 billion women.
48 billion.
About a century has passed. But actually much less than a century has passed because of the overuse here of fudge factors. It really starts getting exponential from there. 72, 18 years, 108, 18 years, 162, 18 years, 243. . .
All these billions will not be volitional/conscious beings that live with integrated honesty. It would be nice to believe that all human beings would have achieved that pinnacle of spiritual evolution in less than a century, but they haven't changed significantly in the last 100 centuries.