Estimating Population Growth(Originally created Jan 2012) |
P = P_{0} * e^[r*t]
Where
P = Population at the end of the interval
P_{0} = Population at the beginning of the interval.
t = Elapsed Time between P_{Start} and P_{End}
e = Base of natural logarithms. (2.71828183)
r = Rate of natural increase in decimal format
The global human population was around 5 million in 8000 BC. What would the human population be in 2000 BC if we used the 4.1793% (in decimal format, remember!) per century rate of natural increase from the April 1986 Bulletin chart below?
First, we define 8,000 BC and 2,000 BC as -8,000 and -2,000 respectively; then subtract them to get a range of 6,000 years, or 60 centuries.
Thus the equation given at the top of this page becomes:
5,000,000 * 2.71828183^[0.041793*60] = 61,375,941
Thus the human population was around 61.3 million in 2000 BC according to these crude calculations.
2012 Wikipedia CalculationsThese rates of increase are based off Wikipedia’s World Population Estimates (LINK) page, with all the various estimates averaged together. |
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Time Frame |
Growth Per Century |
Growth Per Century |
Centuries |
10,000 BC to 4,000 BC |
0.9371% |
0.009371 |
74.31 |
4,000 BC to 1,000 BC |
6.7732% |
0.067732 |
10.58 |
1,000 BC to 1 AD |
16.4563% |
0.164563 |
4.55 |
1 AD to 1000 AD |
1.8411% |
0.018411 |
37.99 |
1000 AD to 1500 AD |
10.3299% |
0.103299 |
7.05 |
1500 AD to 1750 AD |
23.4171% |
0.234171 |
3.29 |
1750 AD to 1900 AD |
65.7685% |
0.657685 |
1.37 |
1900 AD to 1950 AD |
136.1627% |
1.361627 |
0.81 |
1950 AD to 2000 AD |
480.9947% |
4.809947 |
0.39 |
1986 Bulletin CalculationsThese rates of increase appeared in the April 1986 Bulletin of the Atomic Scientists. (Doubling times apparently were calculated via the rule of 72, e.g 72 divided by the growth in percentage points, for example: [72 / 5.6964].) |
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Time Frame |
Growth Per Century |
Growth Per Century |
Centuries |
2,000,000 BC to 50,000 BC |
0.0079% |
0.000079 |
8,774 |
50,000 BC to 10,000 BC |
0.4015% |
0.004015 |
140 |
10,000 BC to 1 AD |
4.1793% |
0.041793 |
17 |
1 AD to 1750 AD |
5.6964% |
0.056964 |
12 |
1750 to 1985 AD |
116.1868% |
1.161868 |
0.6 |
Load up Excel; and use the following formula:
=RATE(Interval, , Pop_{Start},Pop_{End})
where
Interval = Interval in years or days or centuries, or whatever.
Pop_{Start}: Starting population (MUST BE IN NEGATIVE FORMAT!)
Pop_{End}: Ending Population
So if a population grew from 250,000 to 500,000 during a 30 year period, you’d enter:
=RATE(30,,(0-250000),500000)
to get the growth rate.
Doubling Time = (72 / Growth)
Example: A population grows at 0.5% per year. How long until the population roughly doubles?
72 / 0.5 = 144.0 years
T = LN(Interval_{Factor}) / LN(1+r)
Where:
T = Doubling (or tripling, etc) time in the amount used to originally calculate the Growth Rate
Interval_{Factor} = Place a 2 here if you want to know the doubling time, a 3 if you want to know the quadrupling time, etc.
r = The Growth Rate
Example:
A population grows at 0.4015% (0.004015 in decimal) per year. What is it’s doubling time?
LN(2) / LN(1+0.004015) = 173 years