POPULATIONS BY
THE NUMBERS
10,000 yrs ago- 5
1930- 2 billion
1975 – 4 billion
2011 – 7 billion
2050 – 9.5 billion
million
Growing Exponentially
What does it mean to grow
exponentially?
 Youtube. The most important video you’ll ever see
 The Bacteria doubling in a bottle…(22 minutes in.)
Anyone who believes exponential growth can
go on forever in a finite world is either a
madman or an economist" " --Kenneth
Boulding
Population Calculations
Global population
growth rate
= CBR-CDR
10
If there were 20 people born per 1,000
people and 8 deaths per 1,000, the global
population growth rate would be 1.2%
20-8
10
OR
20-8
x100
1000
In 2011, the population growth rate of the
….
world was 1.09%
Zimbabwe = 4.3%
Japan = -0.1%
US = 0.9%
China= 0.5%
India = 1.3%
 To calculate the population growth rate for a single
nation, we take immigration and emigration into
account.
 Nat. pop =
growth rate
(CBR + immigr) – (CDR+ emigr)
10
Population Growth Rate
Annual world
population growth
<1%
1-1.9%
2-2.9%
3+%
Data not
available
Fig. 11.3, p. 240
Doubling Time and the Rule of 70
 If we know the growth rate of a population and
assume that growth rate is constant, we can
calculate the number of years it takes for a
population to double.
Rule-of-70 - way to
calculate the approximate number of years
it takes for the level of a population
growing at a constant rate to double.
 States that the approximate number of years n
for a variable growing at the constant growth
rate of r percent, to double is:
n = 70/r
For example, a city with an
annual population growth rate of
5% will double its population in
approximately 14 years. 70 =14
5
If the growth rate were 7%, it
would double its population in
approximately ? years.
10
Remember that a population growing at 2
percent per year, regardless of the size
will double in 35 years. Whether the
population is 500,000 or 50,000, it will still
double in the same amount of time.
It is almost certain that the Earth’s
population will not double again. Most
demographers believe that the human
population will be somewhere between 8.1
billion and 9.6 billion in 2050 and stabilize
by 2100.

New Zealand has a population of 4.3
million people, a TFR of 2.1 and a
net migration rate of 2 per 1,000.
How many people will New Zealand
gain next year as a result of
immigration? (assume the TFR and
net migrations stays the same)
 Net migration = # of immigrants
rate
# of people in pop
A TFR of 2.1 for a developed country
suggests that the country is at
replacement-level fertility and thus the
population is stable.
 The migration rate suggests that

2__
1000
= __
x_
_
4,300,000
So, X= 8,600 people/year
Since there is no growth due to biological
replacement and a net migration of 8,600 people,
the rate of increase is
8,600 people/year
= 0.2%
4,300,000 people
How many years will it take the population to double
at this rate?
T= 70
r
T=
70
= 350 years
0.2/yr
 A metropolitan region of 100,000
people has 2,000 births, 500 deaths, 200
emigrants, and 100 immigrants over a 1
year period. Calculate its population
growth rate.
 Net increase = 2,100
 Net decrease= 700
 Total change in population=
1400
 Total number in population = 100,000

= 0.014 = 1.4%
 In 2010, the population of Upper Fremont
was 200,000 and growing at a rate of 2%
each year.
 If the rate of population growth remains
constant, calculate the population in
2045.
 Determine the doubling time of the
population by dividing 70 by 2 to get 35
years. Since one 35-year period passes
between 2010 and 2045, the population
would have doubled once from 200,000
to 400,000.
 The population of Lower Fremont was
20,000 in 1968. In 2010 the population
was 160,000. Assuming the growth is
exponential, calculate the average annual
percentage rate of population growth
since 1968.
 2010-1968 = 42 years
 The population has doubled 3 times since
1968. 20,000 → 40,000 → 80,000 →
160,000
 42/3 = 14 years
 T= 70/r
and r= 70/t
 70/14 = 5%
 In 2010, the CBR in East Fremont was 25
and the CDR was 11. Calculate the
percentage growth rate of East Fremont
in 2010. If the population was 15,000 in
2010, and the population growth rate
remains constant, when will the
population reach 30,000?
__CBR-CDR__
14
10
70/1.4
= 1.4%
10
= 50 years
50 years + 2010 = 2060
Population Density
 New York City has 8,175,113 people within
305 mi2.
 Calculate the density of the population in mi2
and km2. 1 km2 = 0.386 mi2
 8,175,113 people = 26,804 people/ mi2
305 mi2
26,804 people x 0.386 mi2
1 mi2
1 km2
= 10,346 people
km2
The population of Atlanta is 420,003 and
covers an area of 131 square miles.
Calculate the density of the population in
in mi2 and km2
420,003 people = 3206 people/ mi2
131 mi2
3206 people x 0.386 mi2
mi2
1 km
= 1238 people/km2
How many times more dense is NYC
than ATL?
10,346 people/mi2 = 3.2 times
3,206 people/ mi2
 The tiny country of Monaco has the
world's highest population density. With
an area of 3/4 of a square mile and a
total population of 32,000, Monaco has a
density of almost 43,000 people per
square mile.
 However, since Monaco and other
microstates have very high densities due
to their extremely small size, Bangladesh
is often considered the most densely
populated country, with more than 2,200
people per square mile.
States by density: New Jersey, Rhode
Island, Massachusetts
States by population: California, Texas,
New York
Cities by population: New York, LA,
Chicago
“The Lily Pond Parable” from EcoFuture
http://www.ecofuture.org/pop/facts/exponential70.html
1. If a pond lily population doubles every day, and
it takes 30 days to completely cover a pond, on
what day will the pond be ¼ covered?
2. If a pond lily population doubles every day, and
it takes 30 days to completely cover a pond, on
what day will the pond be ½ covered?
3. Does the size of the pond make a difference?
4. What kind of environmental consequences can
be expected as the 30th day approaches?
5. What will begin to happen at one minute past
the 30th day?
6. At what point (what day) would preventative
action become necessary to prevent unpleasant
events? Explain your reasoning.
_______________________________________________
Try these for practice…
A. The CBR of a country is 35 and the CDR is 8.
Calculate the population growth rate.
2.7%
B. The population of a city is growing at a rate of
1.7%. It currently has 100,000 people. What will the
population be next year?
101,700
C. A small country of 600,000 people has 15,000
immigrants and 2,500 emigrants. They also experience
8,000 deaths and 5,500 births. What is the growth
rate of this country?
1.67%
D. How long will it take a population to double if the
growth rate is 1.1%
63.64 years
HOMEWORK:
POPULATION CALCULATIONS