Energy and Human Ambitions on a Finite Planet, 2021a

3 Population 32
In more recent years, the rate has fallen somewhat from the 1.7% fit
of the last segment in Figure 3.4, to around 1.1%. Rounding down for
convenience, continuation at a 1% rate would increase population from
7 billion to 8 billion people in less than 14 years. The math is the same as
in Chapter 1, re-expressed here as
P P 0 e ln(1+p)(t−t 0) , (3.1)
where P 0 is the population at time t 0 , <strong>and</strong> P is the population at time t
if the growth rate is steady at p. Inverting this equation, 3 we have
( )
t − t 0 ln P
P 0
ln(1 + p) . (3.2)
3: . . . recalling that that the natural log <strong>and</strong>
exponential functions “undo” each other
(as inverse functions)
Example 3.1.1 We can use Eq. 3.1 to determine how many people we
will have in the year 2100 if we continue growing at a 1% rate, starting
from 7 billion in the year 2010. We set P 0 7 Gppl, 4 t 0 2010, p 0.01,
then compute the population in 2100 to be P 7e ln 1.01·90 17 Gppl.
4: Gppl is giga-people, or billion people
Eq. 3.2 is the form that was used to conclude that increasing from 7 to
8 Gppl takes less than 14 years at a 1% rate. The computation looks The actual time for adding one billion people
has lately been 12 years, as we have been
like: ln(8/7)/ ln 1.01 13.4. Note that we need not include the factors
growing at a rate slightly higher than 1%.
of a billion in the numerator <strong>and</strong> denominator, since they cancel in
the ratio.
Year Population Time Rate Doubling
1804 1 Gppl — 0.4% 170
1927 2 Gppl 123 0.8% 85
1960 3 Gppl 33 1.9% 37
1974 4 Gppl 14 1.9% 37
1987 5 Gppl 13 1.8% 39
1999 6 Gppl 12 1.3% 54
2011 7 Gppl 12 1.2% 59
2023 8 Gppl 12 1.1% 66
Table 3.2: Population milestones: dates at
which we added another one billion living
people to the planet. The Time <strong>and</strong>
Doubling columns are expressed in years.
Around 1965, the growth rate got up to 2%,
fora35yeardoubling time.
Table 3.2 <strong>and</strong> Figure 3.5 illustrate how long it has taken to add each
billion people, extrapolating to the 8 billion mark (as of writing in 2020).
The first billion people obviously took tens of thous<strong>and</strong>s of years, each
new billion people taking less time ever since. Growth rate peaked in
the 1960s at 2% <strong>and</strong> a doubling time of 35 years. The exponential rate is
moderating now, but even 1% growth continues to add a billion people
every 13 years, at this stage. A famous book by Paul Ehrlich called The
Population Bomb [18], first published in 1968, expressed underst<strong>and</strong>able
alarm at the 2% rate that had only increased to that point. The moderation
to 1% since that period is reassuring, but we are not at all out of the
woods yet. The next section addresses natural mechanisms for curbing
growth.
Population (Gppl)
9
8
7
6
5
4
3
2
1
0
1800 1850 1900 1950 2000
year
Figure 3.5: Graphical representation of Table
3.2, showing the time between each
billion people added [14, 15].
© 2021 T. W. Murphy, Jr.; Creative Commons Attribution-NonCommercial 4.0 International Lic.;
Freely available at: https://escholarship.org/uc/energy_ambitions.