# How would I calculate population growth over 300 years with little advancement after an extinction event?

HEAVY EDIT after a few hours sleep and some coffee. Retracting my own answer and adding it to the questioon as it doesn't actually solve my problem and gave me more questions. My logic last night was that I assumed I could use our growth from 1700 to 2020 as a rough model for growth between 2093 (post Earth event) and 2435 (when the story takes place). Question has been reworded to more closely match what I need.

I am coming back to an old SciFi project based a little over 400 year from now. The background involves the decimation of Earth and mass extinction of its species and humanity save for the few that managed to escape and managed to start over on our fledgling interplanetary colonies. Then the main story takes place some 300 years later.

I'm trying to get a good feel for the expected population growth to determine a reasonable number of survivors, or find some means of hand waving the current population. Part of the story includes census data that has relevance to interplanetary politics, so I have already come up with the numbers I want. That said, if assumed population growth would be too high it is easy enough to assume tragedy or population control, but if they are too low I will need to compensate (I'm thinking long term radiation affects or rapid evolution or something increases the prevalence of plural births).

Whatever it could be, I need to know what the population count should be going in both directions.

Note: Total human population goal should be roughly 9 billion around 300 years after the decimation of Earth.

Clarifications:

Colonies exist primarily within our solar system (Venus, Mars, Titan, Europa, etc...). Habitats are slightly different on each body as they have different environments.

FTL tech was developed relatively recently (about 80 years) but it is more like crude jump gates that require a receiving end to be built via non FTL means (basically pre-fab jump gate is assembled by drones after decades of sublight travel). That makes the extra-solar colonies pretty much irrelevant for this question as they will not have more than a generation, which will likely have few births to begin with as they are startup colonies.

While typing up the question I thought of how I might answer it, but I would still like to know other peoples ideas on the subject or if my math is just completely wrong. It is, I didn't account for birth rate, only death rate. Bracketed to not confuse as much. Left answer here to hopefully clarify what I was originally trying for.

In 1700 there was an estimated global population of 682 million people, with a massive mortality rate that caused average age to drop below 35 years old. (this was only average because of high infant and childhood deaths, people still lived reasonably long lives if they made it to adulthood) With the current mortality rate of 7.5 deaths per 1000 people and 300 years we could use the exponential growth formula;
$$y=a(1+b)^x$$
where a = 682,000,000, b = (7.5/1000), and x = 300,
$$y=682,000,000((1+(7.5/1000))^{300})$$ I then get the result of: $$y=6,416,538,709$$ Or roughly 6.4 billion living humans by 2000. However, I am currently planning for a total human population of roughly 9 billion. Assuming medical science has drastically improved, but is also severely handicapped by the rigors of living in space, I would like to simplify the idea to roughly the same current mortality rate of 7.5 per 1000 people. Using the exponential decay formula; $$y=a(1-b)^x$$ where a = 9 billion, b = (7.5/1000), and x = 300 $$y=9,000,000,000(1-(7.5/1000))^{300})$$ I then get the result of: $$y=940,583,032$$ Or roughly 940.6 million original survivors. Both of these scenarios seem to be off as I was hoping for around 500 million or fewer survivors. That means I would likely have to either drastically reduce the death rate or the birth rate.

• Worth looking at previous questions re this sort of problem, especially worldbuilding.stackexchange.com/questions/5186/… Commented Dec 21, 2020 at 10:59
• Wait: are you asking for population numbers, or are you asking about shifting all current science & medicine back 300 years? (They go together, you can't just have modern medicine without biology, neurosciences, chemistry, physics, materials sciences, etc) Commented Dec 21, 2020 at 12:41
• "Bubonic plague is a hoax, I'm throwing a party" Commented Dec 21, 2020 at 15:34
• @elemtilas is right. Technology is a pyramid with the apex depending on everything that has been discovered before. It's really hard to shift that pyramid around. Consequently, if we had today's medical tech 300 years ago, then the only thing different from a practical perspective the difference in dates (if even that). In other words, rather than calling it 1720, you can legitimately call it 2020.
– JBH
Commented Dec 21, 2020 at 15:52
• I am not sure adding your own answer at the end of the question makes any good to it. I find it just more difficult to follow.
– L.Dutch
Commented Dec 21, 2020 at 16:54

Medical science is not the limiting factor, food production and infrastructure building is.

If you give people enough nutritious food and a place to live, and no other task, you can double your population every 15 years. This requires each woman to bear about 8 children, and for them to live to maturity.

You could achieve your 9 billion target population in 300 years from a seed population of only 9000.

The limit is not having children. The limit is having a population that can AFFORD to have children as their primary task.
The bottleneck on your population growth needs to be found not in medical science, but in infrastructure development, and initial habitability of the environment.
I'm pretty sure that even political matters will be a greater impediment to population growth than medical ability. It has been so on Earth, since.... well, since forever.

• Since the OP is looking for a hard-science approach, please back up your statement with relevant citations and formulas
– L.Dutch
Commented Dec 21, 2020 at 16:44
• @L.Dutch-ReinstateMonica Sorry, but the OP has so much edited his own question that it can not even be recognized any more. this INCLUDES the hard-science tag. please delete my answer, it is to a totally different question. Commented Dec 21, 2020 at 16:50
• The OP only added their own answer at the end of the question. This seems to me that makes the question just more difficult to follow, but I don't see it as a change of the question
– L.Dutch
Commented Dec 21, 2020 at 16:53
• Respectfully, no... How would I calculate population growth over 300 years with little advancement after an extinction event?(hard science) is a completely different question than If we had our current level of medical science 300 years ago, how would that affect the population?(science fiction) Commented Dec 21, 2020 at 17:08