math for the expanding population

(no name) ((no email))
Wed, 14 Dec 1994 11:10:27 EDT

After the discussion last week on exploding world population, Eve Pinsker
suggested that i should post the math behind the situation to the net.
This is the first opportunity I have had to do. I am sorry if the thread
has almost evaporated and i ssem to be trying to revive it. for those
who are interested here is the math:

it is based on the exponential function:

dN/N = lambda dt

where N = population
lambda = the exponential constant
t = time.

for the world as a whole the numbers are:
lambda = 1.8%/y **
N in 1993 is 5.7 billion (this figure may be off by a few million to
50 million, because the world census figures for many thrid world nations
are slow to arrive at the bureau that publishes this stuff).

if you do the math, the equation can be modified to
N/No = e^(lambda t)
where No = the population at time 0
e = exponential base e
^ implies an exponent for the stuff in brackets

if we set t = 47 years (2040-1993),

and solve for N, lambda by the way in this expression is ln (1 + 0.018) = 0.0178
N(2040) = 13.18 billion.

now the problem here is that 1.8%/y is not constant. it actually is also growing.
it is a weighted average of the growth rates in each country multiplied by the
population in each country. unfortunately, most of the growth is occurring in
very populous third world countries.

Country Rate of growth (1975)
Bangaldesh 2.8% 79 million in 1975
pakastan 3.0%/y 71 million
Phillipines 3.0%/y 43 million
nigeria 3.0%/y 63 M
braxil 2.9%/y 109 M
mexico 3.1%/y 60
India 2.0%/y 618 M

as these countries' populations increase, their relative strength in the total
world rate of growth becomes stronger and it is itself increasing exponentially

when you add those changes in, then 14-15 billion is the expected growth in
2040, if current trends continue.

someone asked me the effect of the bubonic plague on the growth curve
in the middle ages. estimated world pop at that time was about 500
million +/- 50 million. the plague is estimated to have killed about
15-20% of the population at the time. this did produce a minor blip,
but that effect was nullified within 50-100 years.

we currently double the world population in less than 35 years.
in 1850, it took about 200 years to double the population.

the estimated valued for the global rate of increase in 2040 is 2.2-2.3%/y.
which means a doubling time of < 30 years for 2040. that means that by
2070 world population if unchecked would reach 30 billion assuming
that the growth rate did not increase. if it continued its normal
increase, then by 2060 world pop would be 25 billion, doubling in
< 25 years.

as they say, sometime in 2020-2050 SOMETHING HAS TO GIVE!
so we can do it willingly or we can be forced into it by starvation, plagues,
war, and pestilence. not a nice thought.