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According to Gen 46:27, Jacob entered Egypt with a family of 70. Kohath was Levi's son, Amram Kohath's, and Moses Amram's, so Moses's generation was 2 generations from Kohath's. 600,000 men, with women and children, left at exodus (Ex 12:37).

Meanwhile, before Moses was born, pharaoh ordered, that all male children from then on have to be killed. Moses survived miraculously, so 600,000 has to refer to men from generation above. Roughly estimating, 35 women (half of 70 that entered Egypt), gave birth to 1,200,000 people, which gives a fertility rate of about 34,285 (assuming 0 mortality). This seems quite large. Moreover, if we assume that Jews didn't stop procreating with pharaoh's command, at that fertility rate, there would be about 20 billion women in Moses's generation.

Further, despite lacking partners from same generation, they could be impregnated by their uncles (Moses's mother was the aunt of his father, so it probably wasn't that uncommon), which would push the number even further.

Such numbers are very unlikely, and since Bible is inerrant, can you help me find error in my reasoning?

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    Jews are merely the House of David or the tribes of Judah and Benjamin. I think you mean Hebrew or Israelites, thus all twelve tribes. Yes? – Autodidact Jun 28 at 15:28
  • @RayButterworth sorry, I meant Levi's. That doesn't change anything though. – hcra Jun 29 at 9:30
  • I think you may find an answer in my answer to the question: "What is the biblical basis that Noah died just before the birth of Abraham?" In addition, you could read the online article by Dr John Millam "The Genesis Genealogies - are they complete?" – Andrew Shanks Jun 30 at 17:17
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There are two things you're missing:

  1. The time from Jacob's arrival in Egypt to the nation's liberation under Moses was roughly 400 years.

  2. It is a common (but often missed and misunderstood) practice in biblical genealogies to "telescope" the list of names, focusing only on key individuals in the list. (Going along with this, the word translated as "father" can mean a person's actual parent, or it can mean a more distant ancestor.)

Referring to this source for example, the article states the following concerning the period of time you're looking at:

In the Old Testament period, it was important for every Jew to be able to trace his lineage back to prove his tribal affiliation—it was even more important for Levites and the descendants of Aaron in order to prove they were qualified to be priests (see Ezra 2:59–63). So we can see that in Moses’ day, he is said to be the descendant of Levi, Kohath, and Amram. This is supposed to cover a period of 400 years, and we’re given enough generations to cover just about ¼ of that. That’s not a problem however; the genealogy isn’t concerned with giving an exhaustive list of ancestors; just enough to tell us where Moses comes from. So we have Levi and his son, along with Moses’ father.

So as Cerulean Chelonii noted, the four centuries between Jacob and Moses was plenty of time to allow the population to reach the numbers given at their first census.

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    Though the question specifically asks for Jews, Bible says there was a mixed multitude beside the Hebrew people that went out too. Exodus 12:38. So the number could very well have exceeded conservative numbers. – Autodidact Jun 29 at 5:03
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Human population growth often takes the form of exponential growth, which can be modelled with the following mathematical formula:

P = P0 × er × t

Where:

  • P is the final population
  • P0 is the initial population
  • e is Euler's number (approximately 2.71828)
  • r is the growth rate
  • t is the time duration

In this case, we are interested in the growth rate. This can be determined by rearranging this formula using logarithms and a little algebra:

r = ln(P ÷ P0) ÷ t

Now, if we plug in the numbers we already know, we should be able to calculate the growth rate. The Bible states that 70 Isrealites entered Egypt (Genesis 46:27), they remained there for 400 years (Genesis 15:13), and then they left with a total of 600,000 men, not including woman and children (Exodus 12:37). To include women, we can double the population of the men to produce 1,200,000. If we reduce the number of years from 400 to 380, we can ignore the children:

r = ln(1,200,000 ÷ 70) ÷ 380

r = 0.02565615

r = approximately 2.57%

Ultimately, we can see that this yields a growth rate of about 2.57%. This appears to be a fairly normal growth rate. According to Wikipedia, the modern global growth rates is about 1.09%, with different countries ranging between -1.03% and 4.26% (it appears that poorer countries tend to have higher growth rates).

I am by no means an expert in this field, so if I made a mistake anywhere, please feel free to correct me. In any case, from these calculations, it appears that the population growth that the Israelites experienced during their time in Egypt is fairly reasonable.

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