# How did we get so many people in such a short time?

sxc.hu/mzacha

##### First published: 13 April 1998 (GMT+10)

Re-featured on homepage: 2 October 2013 (GMT+10)

##### Updated: 11 September 2013

To work out how quickly a population can grow, it’s very important to understand *exponential growth*. Starting from eight people after the Flood, the population would have to double only 30 times to reach 8.6 billion. Now there is a well-known ‘Rule of 72’,^{1} which says divide 72 by the percentage growth rate to get the time required for doubling. E.g. if inflation is 8% p.a., then in ^{72}/_{8} = 9 years, the cost of living will have doubled.

So what is a realistic growth rate? The *Encyclopaedia Britannica* claims that by the time of Christ, the world’s population was about 300 million. It apparently didn’t increase much up to AD 1000. It was up and down in the Middle Ages because of plagues etc. But may have reached 800 million by the beginning of the Industrial Revolution in 1750—an average growth rate of 0.13% in the 750 years from 1000–1750. By 1800, it was one billion while the second billion was reached by 1930—an average growth rate of 0.53% p.a. This period of population growth cannot be due to improved medicine, because antibiotics and vaccination campaigns did not impact till after WWII. From 1930 to 1960, when the population reached three billion, the growth rate was 1.36% p.a. By 1974, the fourth billion was reached, so the average growth rate was 2.1% from 1960 to 1974. From 1974 to 1990, when the mark hit five billion, the growth rate had slowed to 1.4%. World population reached 6 billion in 1999 and 7 billion in 2011. The increase in population growth since WWII is due to fewer deaths in infancy and through disease.

If the average growth rate were a mere 0.4%, then the doubling time would be 180 years. Then after only 30 doublings or 5400 years, the population could have reached over eight billion.

If you want something more rigorous, there are standard mathematical formulæ that can be used to calculate population growth. They must include birth and death rates as well as generation time. The simplest formula involves just a constant growth rate:

N = N_{0}(1 +^{g}/_{100})^{t}

where N is the population, N_{0} is the initial population, g is the percentage growth rate per year, and t is the time in years. Applying this formula to the population of eight surviving the Flood, and assuming a constant growth rate of 0.45% p.a. and 4500 years:

N = 8 (1.0045)^{4500}= 4.8 billion people.

Of course, the population growth hasn’t been constant, and would have been very fast just after the Flood. Thus this formula by itself cannot be used to prove a young earth. However, if the world’s population had been in the millions for 100,000 years, then where are all their bodies? (See also 101 evidences for a young age of the earth and the universe, section ‘Human history is consistent with a young age of the earth’.)

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- More precisely, the formula is: doubling time =
^{100 ln2}/_{g}, where ln2 is the natural logarithm of 2 (0.693) and g the percentage growth rate. So it would be slightly more precise to use a ‘Rule of 69’, but 72 is chosen because more numbers divide evenly into it, and it is good enough for an approximate rule of thumb.

(The rule is also handy for calculating the doubling time of a debt or investment, using the percentage interest rate instead. This is a little more complex because the population case is analogous to continuously compounded interest, while in finance the interest might be compounded annually. But here the precise number is closer to 72 than in the population case. See The Rule of 72—Why it Works.) Return to text.

(Also available in Spanish.)

Very timely. And even if we can't know all the growth rates from the flood to today, this article helps us in general understand that the earth isn’t 15 billion years old based on guess-ta-mates by our secular scientists. Keep up the good work.

I also am doing my family tree BUT in my case my in my father's father's family, the men tend not to marry but remain childless and so the family name is disappearing. In my father's mother's tree the men did the same thing, and the one remaining man who did marry had 5 daughters and bingo the name was gone forever in that branch of the family.

A beautifully logical article.

But we need to be humble in our search for answers. Not ever premise in a discussion is necessarily accurate or true. So, our logical conclusions can only be as good as the premises on which they are based.

For me, I have only a handful of Truths.

I hold that God is love. I hold that Jesus came to rescue us.

But I wonder about the premise that death did not exist before the sin in the Garden. Why?

Because death does not equal death. Adam's death on the day he ate of the forbidden fruit was a spiritual death—not a physical one. Just as the rebirth Jesus described to Nicodemus was not a physical rebirth. We must be reborn of the spirit.

If we remain humble, we may discover all manner of new Truths in the Bible. Too many have become lazy and arrogant, clinging to the literal—the easy. But as 2 Corinthians 3:6 cautions us, the literal (letter) leads to death; only the spirit will lead to life. The literal in scripture is a guidepost for where to dig. If you do not dig, you will never find the spirit within.

A strange sort of ‘spiritual death’ is Adam returning to the dust (Genesis 3:19). Then, since Paul relates Jesus’ death and resurrection to Adam's death in 1 Corinthians 15, did Jesus only die and rise spiritually as well? It's important to understand here that when we have 'spiritual bodies’, this means ‘*controlled *by the spirit’ not ‘composed of spirit’.

Evidently the ‘literal’ (which in reality is the grammatical-historical or originalist) interpretation is *not* easy for those who want to compromise with the millions of years of evolutionary uniformitarianism.

You also manage to misconstrue 2 Corinthians 3:6. The ‘letter’ has nothing to do with literal interpretation, but stands for the Law of Moses (a figure of speech called *synecdoche*). As the passage says, “He has made us competent as ministers of a new covenant—not of the letter …”, that is, the *new *covenant not of the letter contrasts with the *old *covenant which was of the letter, clearly the Law.

The ‘spirit’ doesn't mean any supposed ‘spiritualized’ interpretation that loses all objective connection to the text. Rather, it refers to the *Gospel*. This is what gives eternal life; compare John 6:63, Romans 8:2, 10.

Hello Jonathan,

This is easy to understand for anyone who has done family history. My G-G-Grandfather was born 1810, married 1832. He came to Australia in 1840, and also one of his nephews. I have traced 1235 descendants in Australia, and have not found them all (I also decided to forget the Smiths). He was 1 of 8 children, so the descendants of the family is in the order of 10,000 in 180 years.

"The increase in population growth since WWII is due to fewer deaths in infancy and through disease," which is more than offset by the number of children that are murdered through abortion.

The real question is why are there so little people after such a long time if the human population is more than a million years old. Lets say that the first 2 humans appeared one hundred thousand years ago, and that the human population doubled after every 1,000 years. That’s an absurdly low growth rate. After one hundred thousand years, there would be 10^{30} people. There's about 10^{18/ inches on the earth, so that's about 1012, or a trillion people per square inch.}

Of course, the earth would be filled, as per the reason God told Adam and Eve to multiply, long before this.

Hi Dr. Sarfati,

Mathematically speaking, what could be taken into account to adjust the formula in order to get a number closer to the current population of >7 billion? I am currently taking an Environmental Issues class at my university and we have been discussing population growth. My professor is an Old-Earth Creationist, but I think that he would certainly be interested in discussing this.

The most detailed paper was published only last year, i.e. long after the article above: Carter, R. and Hardy, C., Modelling biblical human population growth, *J. Creation* **29**(1):72–79, 2015.

G’day Jonathan,

Great article and one that also indirectly suggests a major catastrophe somewhere in earth's history e.g. Noah’s Flood.

Based on the estimates for growth if there had not been a halt to the population growth from the time of Adam and Eve there would be standing room only on Earth today given that an additional 1,500 years of procreation had taken place!

Best Regards,

Roger.