Assume the earth gets destroyed in 2165 and the humans that would have survived move to a new planet.
Context: Humans mastered interstellar travel 80-90 years ago, after warp technology was developed, but before the planet's demise. They have founded a few colonies of a few thousand colonists (mining and agriculture), They had already established a new planet as their main colony planet with about 50,000 -70,000 colonists before the earth-death.
The humans and their alien allies start to evacuate earth with merely 2 weeks warning.
The population of the earth at the time was ~10 billion, which drove their colonization push. It is about to drop greatly, saving merely ~ 19 million humans. Full ships head out, drop off colonists, then come back for another load.
After the planet is gone, survivors are taken to the new homeworld and allied worlds. There they'd all be registered for a head-count of survivors and assigned supplies while they deal with the mess. Since humans are quite advanced and would rely heavily on their alien allies for aid, they'd have access to medical supplies, emergency homes and advanced technological equipment.
Abortions are illegal; embryonic transfer to an artificial womb is possible however, at a certain gestational development. Infant care is too costly, but people donate their DNA to a sort of gene bank for future diversity.
200 years later, the human population is back on their feet. What is their population now?
Math is not my strong suit, a little help please.
So, What would the approximate human population be in 2365?