Doubling Time - Examination

Examination

Examining the doubling time can give a more intuitive sense of the long-term impact of growth than simply viewing the percentage growth rate

For a constant growth rate of r%, the formula for the doubling time Td is given by

≈

Some doubling times calculated with this formula are shown in this table.

Simple doubling time formula:

  • N(t) = the number of objects at time t
  • d = doubling period (time it takes for object to double in number)
  • c = initial number of objects
  • t = time
Doubling times Td given constant r% growth
r% Td
0.1 693.49
0.2 346.92
0.3 231.40
0.4 173.63
0.5 138.98
0.6 115.87
0.7 99.36
0.8 86.99
0.9 77.36
1.0 69.66
r% Td
1.1 63.36
1.2 58.11
1.3 53.66
1.4 49.86
1.5 46.56
1.6 43.67
1.7 41.12
1.8 38.85
1.9 36.83
2.0 35.00
r% Td
2.1 33.35
2.2 31.85
2.3 30.48
2.4 29.23
2.5 28.07
2.6 27.00
2.7 26.02
2.8 25.10
2.9 24.25
3.0 23.45
r% Td
3.1 22.70
3.2 22.01
3.3 21.35
3.4 20.73
3.5 20.15
3.6 19.60
3.7 19.08
3.8 18.59
3.9 18.12
4.0 17.67
r% Td
4.1 17.25
4.2 16.85
4.3 16.46
4.4 16.10
4.5 15.75
4.6 15.41
4.7 15.09
4.8 14.78
4.9 14.49
5.0 14.21
r% Td
5.5 12.95
6.0 11.90
6.5 11.01
7.0 10.24
7.5 9.58
8.0 9.01
8.5 8.50
9.0 8.04
9.5 7.64
10.0 7.27
r% Td
11.0 6.64
12.0 6.12
13.0 5.67
14.0 5.29
15.0 4.96
16.0 4.67
17.0 4.41
18.0 4.19
19.0 3.98
20.0 3.80

For example with an annual growth rate of 4.8% the doubling time is 14.78 years, and a doubling time of 10 years corresponds to a growth rate between 7% and 7.5% (actually about 7.18%).

When applied to the constant growth in consumption of a resource, the total amount consumed in one doubling period equals the total amount consumed in all previous periods. This enabled US President Jimmy Carter to note in a speech in 1977 that in each of the previous two decades the world had used more oil than in all of previous history, because of the roughly exponential growth in world oil consumption between 1950 and 1970 with a doubling period of under a decade.

Given two measurements of a growing quantity, q1 at time t1 and q2 at time t2, and assuming a constant growth rate, you can calculate the doubling time as

Read more about this topic:  Doubling Time

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