the matrix - How does Zion population square with how it's built?

The Architect says that The One must choose 23 people (16 female, 7 male) to create new Zion.

After which, you will be required to select from the Matrix 23 individuals - 16 female, 7 male - to rebuild Zion.

But this doesn't seem to make any sense considering the following two statements (listed in un-cited form on Matrix Wikia)

1. 
   

   Zion, according to the Architect, has been completely destroyed five times by the time of the sixth One, Neo, meets the Architect. As a result, the actual year on Earth is estimated to be closer to 2699, not 2199.

   
   

   This means that Zion grows to its final pre-destruction size in only 100 years.

   
   


2. 
   
   

   Yet, the current Zion has - at least according to Wikia - a population of over 250,000 humans.

   
   

How can one square those 3 facts?

It seems completely impossible to both generate a population of quarter million, AND all that advanced Zion infrastructure, in just the space of under 5-6 generations (100 years) if you start with 23 people. (Even allowing for non-natural population growth - i.e., culling out people from the Matrix, the way Neo was extracted. That seems a very labor intensive and non-scalable process - one ship can not extract more than a couple of people a day given its size and medical facilities).

Is there some canon explanation for this discrepancy? Are one of the two facts that Wikia lists incorrect/noncanonical? Did Architect lie to Neo? Do the machines somehow help build up Zion and populate it further?

Answer

Even in the present day, there are some countries with birth rates of ~7 children per generation. It's also not clear what the rates of extraction are; if the founders could manage an extraction a month for the first decade, and kept up the 2/1 male-to-female ratio, they could cut the births-of-women per woman down to about 5.15 to get 250k population after ~5 generations. If they could additionally maintain a skewed gender ratio, this could be consistent with what's observed today.

Thus, while certainly not consistent with lifestyle in modern industrialized countries, it is not completely impossible.

Here's an example scenario, assuming a first child at 15, two children every five years (equally likely to be male or female), a last child at 40 (a total of 11), that people are extracted at age 18 (including the founders) and are extracted once per month for the first 15 years, twice for the next 15, three times for the next 15, etc., that lifespan is 75, and that all extractions and births are gender-balanced:

However, even though this generates the right number of people, the age distribution is kind of screwy; the median age is 11. Still, there are a non-negligible number of adults (~100k over 15).