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

##### 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’.)

Re-featured on homepage: 2 October 2013

### References and notes

- 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.

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