Quote:
Originally posted by Luvian:
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The colony is 40 years old. At first they had enough material to create 10k child. They were supposed to have a reproduction phase when they reached 20, and then another when those new child would reach 20 too. That's 2 generation. But from those 10k, 40 years later, there more than 100k people. We also learn that they are at their 4th generation. This mean they probably start having sex when they are 10 years old! or they wouldn't have time to have 4 generations in 40 years. To get to 100k people from 10k in 40 years, every female would also need to have a lot of children...)
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So, I've made this my problem of the day...and here's the assumptions the author made, if they ever broke out a calculator and figured things out...
1)All females will produce one child a year...This isn't completely true, the rate could be slightly higher (4/3 children per year, max...and that's medically impossible)...but 1 per year makes the calculations easier, and allows for some health care that would keep production going more smoothly.
2)50% of the initial population is female, 50% of all children produced are female.
3)Mortality rates are zero, fertility rates are 1.
Given that, we find that:
{population as a function of time, in thousands of people and in years}
From t=0 to t=20, P(t) = 10
From t=20 to t=40, P(t) = 10 + 5 (t - 20)
This yields 110 thousand people at 40 years.
Personally, considering the particulars of the population, I would think they would begin "production" a little earlier, so, in my estimates, I used 15 years old, for simplicity in the math, and for other reasons based upon the scenario outlined in your description of the society.
thus,
From t=0 to t=15, P(t) = 10
From t=15 to t=30, P(t) = 10 + 5(t - 15)
From t=30 to t=45, P(t) = 10 + 5(t - 15) + 5(t-15)(t - 30)
This would yield a population of 1385 thousand, or 1.385 million people in 40 years.
That third generation is where such a population really starts to take off...
The problems with this kind of population, besides the ethical and logistic ones (which are significant!) is that it is increasingly female, and the average age goes lower and lower.
Incidentally, for times past the third generation, I haven't bothered to work out, but it seems like a fun little exercise...just don't try to extend it indefinitely, or you'll have to use differential equations, and try and factor in death rates!