2. Population Growth – Israel in Egypt

Interest in Noah and the Great Flood has never been greater due to the recent worldwide release of Noah, the Movie, starring Russell Crowe, in March 2014.

The movie graphically portrayed the devastation of Noah’s Flood, but it did not address a very intriguing question: How many people died in Noah’s Flood?

This Population Growth series will suggest an answer to that question.

Was it possible for Noah’s family to reach today’s 7 billion in only 4500 years since the Flood? Yes, easily, because population growth is compound growth like compound interest. Populations grow exponentially, just like money in a savings account.

The previous post Could Noah Fill the Earth? showed that an annual growth rate of only 0.465% was needed for the population to grow from 6 people (Noah’s 3 sons and their 3 wives) to 7.1 billion people in 4,500 years. This is a reasonable and easily attainable growth rate based on historical comparisons.

Israel Leaving Egypt
Scene from The Ten Commandments, 1956 movie by Paramount Pictures

Israel in Egypt

Populations can grow much more rapidly than the 0.465% average growth rate calculated from the time of the Flood to get the present Earth’s population. An example is the growth of Jacob’s family into the nation of Israel in Egypt in 430 years (Exodus 12:40-41).

Then Jacob arose from Beersheba; and the sons of Israel carried their father Jacob and their little ones and their wives in the wagons which Pharaoh had sent to carry him. They took their livestock and their property, which they had acquired in the land of Canaan, and came to Egypt, Jacob and all his descendants with him: his sons and his grandsons with him, his daughters and his granddaughters, and all his descendants he brought with him to Egypt. (Genesis 46:5-7)
All the persons belonging to Jacob, who came to Egypt, his direct descendants, not including the wives of Jacob’s sons, were sixty-six persons in all, and the sons of Joseph, who were born to him in Egypt were two; all the persons of the house of Jacob, who came to Egypt, were seventy. (Genesis 46:26-27)
Now these are the names of the sons of Israel who came to Egypt with Jacob; they came each one with his household: (Exodus 1:1)

Thus the initial Israelite population in Egypt numbered about 100:
1 (Jacob) + 3 (Jacob’s wives) + 66 (Jacob’s descendants from Canaan)
+ 3 (Joseph and his 2 sons in Egypt) + 12 (wives of Jacob’s 12 sons)
+ 15 (estimate for clan concubines and wives of Jacob’s 51 grandsons)

The final summand of 15 is a guess; the others are exact. At least two of Jacob’s sons, Simeon (Genesis 46:10) and Judah (Genesis 38) had concubines that bore them children. At least two of Jacob’s middle grandsons had wives, and likely a number of others since Jacob was age 130 when he went to Egypt (Genesis 47:9). The only result of 15 being too large an estimate is that the calculated growth rate using 15 will be slightly smaller.

In Egypt this clan of 100 and their descendants bred like rabbits:

But the sons of Israel were fruitful and increased greatly, and multiplied, and became exceedingly mighty, so that the land was filled with them. Now a new king arose over Egypt, who did not know Joseph. And he said to his people, “Behold, the people of the sons of Israel are more and mightier than we. “Come, let us deal wisely with them, lest they multiply and in the event of war, they also join themselves to those who hate us, and fight against us, and depart from the land.” So they appointed taskmasters over them to afflict them with hard labor. And they built for Pharaoh storage cities, Pithom and Raamses. But the more they afflicted them, the more they multiplied and the more they spread out, so that they were in dread of the sons of Israel. (Exodus 1:7-12)

How large did Jacob’s family grow by the time they left Egypt 430 years later? Moses took a census near the start of the second year after they left Egypt (Numbers 1:1-3). The total number of fighting men aged 20 years old and upward was 603,550 able-bodied men, fit for war. (Numbers 1:45-49)

To estimate the total population of Israel, I need to add to Israel’s 603,550 able-bodied men the able-bodied men in the tribe of Levi which was not counted in the census (Numbers 1:47-49) plus women, children, and the elderly.

Tribe of Levi: I will estimate the number of able-bodied men in the tribe of Levi by using the average of the other 12 tribes – 50,296 (Numbers 1:5-47). This brings Israel’s estimated total of healthy men fit for battle to 653,846.

Women: Assume there are about the same number of able-bodied women as men – 653,846. Including the able-bodied women, this brings Israel’s estimated total of able-bodied people to 1,307,692.

Elderly: Assume “able-bodied men fit for war” covers the age range of 20 to 65 years. Using 2010 U.S. Census data to calculate the ratio of the 65 and older U.S. population to the 20- to 65-year-old U.S. population, one finds the percentage is 21.74%. Thus I will use 20% of Israel’s able-bodied 20+-year-old population to estimate the number of elderly Israelites. This gives an estimate of 261,538 for the elderly. Including the elderly, this brings Israel’s estimated total to 1,569,230.
(See Table 2 (p.4) in 2010 U.S. Census: Age and Sex Composition and Table 1 (p.2) in 2010 U.S. Census: The Older Population.)

Children: Jacob had 12 sons and those 12 sons had themselves sired 53 sons by the start of their Egyptian sojourn (Genesis 46:8-27). For these original 13 fathers, this is an average of 5 sons per father. Assuming families in Egypt continued reproducing sons at this rate and had about as many girls as boys, it would mean each family averaged 10 children. The number was probably greater than this since Scripture marvels at the fruitfulness of the Israelites. They had even surpassed the native Egyptian population in numbers — so much so that the Egyptians were in dread of the Israelites (Exodus 1:9,12). Nevertheless, for estimation purposes, I will use a conservative lower average of 6 children per family.

How many families? Reduce the potential 653,846 able-bodied families by 53,846 to account for the unmarried. This assumes about 8% of the able-bodied population never married and never produced children. Then there would be 3,600,000 children for 600,000 families. This brings Israel’s estimated total population to 5,169,230.

Thus 5 million people is a reasonable conservative estimate for Israel’s population one year after the Exodus.

For a population increase from 100 people to 5 million people in 431 years, the doubling time would be 27.6 years, and the annual growth rate would be 2.54%. This is one of the highest known growth rates in post-Flood history. For comparison, the global annual growth rate peaked at 2.2% in 1963. The estimated Israelite growth rate, while greater than the maximum global rate, is certainly possible.

Population Growth Formulas

For those interested in checking the math, here are the relevant Population Growth formulas:
Starting with population P, the new population is
= P x 2^d after d doublings.
= P x (1+r)ⁿ after n years at an annual growth rate r.

The population doubling time in years is
= T/d where T is the population’s elapsed time in years and d is the # of doublings.
= (log 2) / log(1+r) where r is the annual growth rate.

Questions to Ponder

1. The estimate of 5 million for the number of Israelites leaving Egypt is a lower bound; the number was probably much larger. What would it be if Israeli families averaged 12 children in Egypt instead of only 6 as the calculation above assumes?
2. Why do Americans have so few children these days? Is this change Biblical?

Share your thoughts on these questions in the comments below. It could encourage or help another reader.

Soli Deo Gloria.

Read the prequel in this series on Population Growth:
1. Population Growth – Could Noah Fill the Earth?

Read the sequels:
3. Population Growth – Challenge to Evolution
4. Population Growth – How Many Died in Noah’s Flood?

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©William T. Pelletier, Ph.D.
“contending earnestly for the faith”
“destroying speculations against the knowledge of God”
(Jude 1:3; 2 Cor 10:4)
Wednesday June 4, 2014 A.D.

But the sons of Israel were fruitful and increased greatly, and multiplied, and became exceedingly mighty, so that the land was filled with them. Now a new king arose over Egypt, who did not know Joseph. And he said to his people, “Behold, the people of the sons of Israel are more and mightier than we. (Exodus 1:7-9)