How high could a population of 100 million people rise in 30 years, living on a terraformed planet with more or less limitless resources and advanced life-prolonging nanotech?
Up to 2-3 billion
Assuming they were really into child birth, and half were female, they could have one baby every 9 months on average, use advanced healing to recover, and repeat. That means 40 generations of 50 million babies, which is 2 billion. When their children were 18 some could join in.
That said, not all women are likely to want to constantly be pregnant, so less births are likely. 2-3 billion is the likely cap.
The highest population rates registred are around 3% to 4%.
These numbers came from natural growth, without migration.
So, 3.5% per year in 30 years increase the population in 180%. The 100 million turn in 280 million.
This scenario looks like countries in first to second step of demographic transition: high fertility rate while child mortality is in the ground.
To force women of the planet give birth in a high rate you will need some despotic ruler, and also make their workforce unecessary.
Btw, since your planet have tons of nanotech to prolong life perhaps they have some kind of artifitial womb and some Star Wars's Kamino clone factory technology, or the baby factories of Brave New World. This would make the growth rate skyrocket to any number of you desire.
In 1950, the population of Earth was some 2.5 billion people. 30 years later, in 1980, it was around 4.5 billion. A period of comparatively limitless resources (compared to the population and abundance of resources, there was no lack of resources during this period), and it was during a period of exponentially decreased mortality and lengthening of the human life span.
To prevent osteoporosis and have good enough recovery woman can give birth of 8 childrens every year - 6 month pregnacy and then early birth and child grow with nanotech help.
50 milion womans * 8 kids = 400 milion kids every year. And so on for 10 Years - 4 bilon kids. Why 10 Years? After 10 Years with nanotech help kids will be grow enough to have kids.
- 11 year have 2.4 bilion births, total population 6.5 bilion
- 12 - 4 bilion, TP - 10.5B
- 13 - 5.6 bilion, TP - 16.1B
- 14 - 7.2 bilion, TP - 23.3B
- 15 - 8.8 bilion, TP - 32.1B
- 16 - 10.4 bilion, TP - 42.5B
- 17 - 12 bilion, TP - 54.5B
- 18 - 13.6 bilion, TP - 68.1B
- 19 - 15.2 bilion, TP - 83.3B
- 20 - 16.8 bilon, TP 100.1B
- 21 - 26 bilion, TP 126.1B
- 22 - 42 bilion, TP 168.1B
- 23 - 64.4 bilion, TP 232.5B
- 24 - 93.2 bilion, TP 325.7B
- 25 - 128.4 bilion, TP 454.1B
- 26 - 170 bilion, TP 624.1B
- 27 - 218 bilion, TP 842.1B
- 28 - 272.4 bilion, TP 1113.5B
- 29 - 333.2 bilion, TP 1446.7B
- 30 - 400.4 bilion births, total population 1.8467 trilion peoples.
This is theoretical maximum with extend use nanomachines and drugs, without use of incubators, artifical utreus, oviary extraction and modification.
Do not even ask about ethics.
Depends on the demographics of your people and their motivation.
One factor is age distribution. You want to know what percentage of you population is of child-bearing age. This tends to be 18 at the lower end for cultural reasons, and 40-45 at the upper end for biological reasons. The lower end is unlikely to change much, but the higher one might depending on precisely how this life-prolonging tech works. In a typical rich nation today this might be around 25-30% of the population, but with luck or good planning the proportion of your colonists might be close to 100% - at least until the children start being born, that is.
Gender distribution also matters. In most cases you'd have a somewhat equal distribution of me and women, but the number of working wombs is a bottleneck here. The higher the proportion of your population are women, the more growth you can have (up until you start having difficulty getting enough sperm samples to go around, but you'd have to get lower than 1% men before that is a big problem). It's unlikely you'd get that distribution on your first wave of colonists, but with the limitless resources having artificial insemination and selecting for gender shouldn't be a problem so I'll assume all future generations are 99% women.
I've run a short python simulation under these numbers to see what we'd end up with. I'm assuming one birth per woman per year, partly because you need recovery time and partly because it makes calculations easier. After 30 years you have 650 million adults and 4.761 billion children, for a total of almost five and a half billion people. Hope those limitless resources include robot nannies.
If you instead assume (perhaps more realistically) one child every two years, numbers drop to 350 million adults and 1415250000 children, for a total of 1.77 billion people.
All this is just a theoretical maximum, assuming your colonists had as their highest motivation to maximize their population to the detriment of all other pursuits. If you find a hundred million people willing to to that, and convince their children to do the same, you'd get these numbers. In any other scenario, the numbers will be lower - likely a lot lower.