Population Growth Of Various Countries
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Transcript of Population Growth Of Various Countries
Population Growth Of Various Population Growth Of Various CountriesCountries
Jose Henson
Sam Choi
Natalie Wagner
Alex Kang
Origins of Population Growth Models
• Thomas Malthus proposed that human growth would precede exponentially– An essay on the principle of population as it
affects the future improvement of society (1798)– Gave formula:– Growth Rate:
– Predicted the world would soon outgrow its resources, with the ultimate destruction of mankind
rtif eP=P
rP=dt
dP
Exponential GrowthExponential GrowthExponential Population Growth:
-Used for rapidly growing population
- Bacteria, insects, rabbits
-Assumptions
-All individuals reproduce constantly and equally
-Not valid for human population growth
- Valid over a short period of time
rtif eP=P
Growth of BacteriaGrowth of Bacteria
• Reproductive rate, r, is found from data by finding ratio of 2
• Exponential growth equation can now be used to calculate future populations
• At t=100
Time (Min)
Bacteria Cells
0 1000
10 2000
20 4000
30 8000
40 16000
50 32000
60 48000
2re 69314.r
rtif eP=P
8069314.1000e=P2710208.1 P
Revision of the Population Revision of the Population ModelModel
• Pierre-Francois Verhulst of Belgium - Suggested that there was a limit to population growth in 1838- Growth Formula:
- mu represents mortality caused by high population
-as population increases growth is overshadowed
2PrP=dt
dP
Modern NotationModern Notation
M
PrP=
dt
dP1 PMP
M
r=
dt
dP
r
M
2PrP=dt
dP
Factor from both termsrP
Verhulst’s Logistic growth model:
P
rrP=
dt
dP 1
Substitute
or
Population ModelPopulation Model
PMPM
r=
dt
dP
rdt
dP
PMP
11
CrtPMP lnln
Population equation can be found by solving the differential equation
Algebraic manipulation:
Integrate with respect to t:
CrtP
PM
lnSimplify:
Derivation ContinuedDerivation Continued
Crt eeP
PM
CeP
PM rt
AeP
M rt 1
rtAe
MP
1
Exponentiate:
Let :CeA
Simplify:
Solve for P:
Logistic Population GrowthLogistic Population Growth
Logistic Population Growth :
M = Population Capacity
A = Initial Population Constant
r = Reproductive rate constant
Assumptions:
- Found via logistic regression line
- Only valid over long periods of time
rtAe+
M=P 1
Calculating Regression Calculating Regression EquationsEquations
Linear Regression:
- Commonly called “best fit” line
Logistic Regression
- Creates a “best fit” S-shaped curve
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
0 1 2 3 4 5
Population of the WorldPopulation of the World
Current Population:
6,442,658,699 people
Growth Rate:
76,570,430 people per year
Estimates:
2020: 7.6 Billion people
2030: 8.2 Billion people
2050: 9.1 Billion People
United StatesUnited States
Y 9E8 ln x 7E9
te+=P
.01402.1751.000
854.1
Population of United States
0
50
100
150
200
250
300
350
0 10 20 30 40
Year
Po
pu
lati
on
(M
illio
ns
)
Analysis of Population LevelsAnalysis of Population Levels
154.3022.1751.000
706.135.0140
e+=P
100734.295
154.302734.295%100
Actual
alExperimentActualError
te+=P
.01402.1751.000
706.1
Calculated Current Population at t=35 (In Millions)
Actual Current Population = 295.734 Million People
%36.2Error
Analysis of Population GrowthAnalysis of Population Growth
22.1751.014
1.01421.501
)+(
)(=
dt
dPt
t
%100P
dtdP
10092.
8187.92.%100
Actual
alExperimentActualError
Current Population Growth at t=35
Growth Rate:
%01.11Error
4211.22.1751.014
1.01421.501235
35
)+(
)(=
dt
dP
8187.%100734.295
4211.2
South KoreaSouth Korea
te+=P
.0454.7421.00
55.9
Population Of South Korea
0
10
20
30
40
50
60
0 10 20 30 40
Year
Po
pu
lati
on
(M
illio
ns
)
Analysis of Population Levels
te+=P
.0454.7421.00
55.9
Calculated Current Population at t=35 (In Millions)
546.48.7421.00
55.935.0454
e+=P
Actual Current Population = 48.422 Million People
100546.48
546.48422.48%100
Actual
alExperimentActualError
%256.Error
Analysis of Population GrowthAnalysis of Population Growth
2932..7421.046
1.0461.883235
35
)+(
)(=
dt
dP
235
35
.7421.046
1.0461.883
)+(
)(=
dt
dP
%100P
dtdP
Current Population Growth at t=35
Growth Rate:
%0606.%100422.48
932.2
10038.
606.38.%100
Actual
alExperimentActualError
%34.59Error
JapanJapan
te+=P
.083.2441.000
129.331
Population Of Japan
0
20
40
60
80
100
120
140
0 10 20 30 40
Year
Po
pu
lati
on
(M
illio
ns
)
Analysis of Population LevelsAnalysis of Population Levels
100417.127
626.127417.127%100
Actual
alExperimentActualError
626.127.2441.000
129.33135.083
e+=P
te+=P
.083.2441.000
129.331
Calculated Current Population at t=35 (In Millions)
Actual Current Population = 127.417 Million People
%164.Error
Analysis of Population GrowthAnalysis of Population Growth
2.2441.087
1.0872.619
)+(
)(=
dt
dPt
t
%100P
dtdP
100107.
107.05.%100
Actual
alExperimentActualError
Current Population Growth at t=35
Growth Rate:
1376..2441.087
1.0872.619235
35
)+(
)(=
dt
dP
%1078.%100626.127
1376.
%69.115Error
IndiaIndia
te+=P
.03502.6731.000
1952
Population Of India
0
200
400
600
800
1000
1200
0 10 20 30 40
Year
Po
pu
lati
on
(M
illio
ns
)
Analysis of Population LevelsAnalysis of Population Levels
100264.1080
426.1093264.1080%100
Actual
alExperimentActualError
426.10932.6731.000
195235.0350
e+=P
te+=P
.03502.6731.000
1952
Calculated Current Population at t=35 (In Millions)
Actual Current Population = 1080.264 Million People
%218.1Error
Analysis of Population GrowthAnalysis of Population Growth
22.6731.036
1.036182.619
)+(
)(=
dt
dPt
t
%100P
dtdP
1004.1
556.14.1%100
Actual
alExperimentActualError
Current Population Growth at t=35
Growth Rate:
806.162.6731.036
1.036182.619235
35
)+(
)(=
dt
dP
%556.1%100264.1080
806.16
%143.11Error
Population Of South Korea
0
10
20
30
40
50
60
0 10 20 30 40
Year
Po
pu
lati
on
(M
illio
ns
)
Population Of The United States
0
50
100
150
200
250
300
350
0 10 20 30 40
Year
Po
pu
lati
on
(M
illio
ns
)
Population Of Japan
0
20
40
60
80
100
120
140
0 10 20 30 40
Year
Po
pu
lati
on
(M
illio
ns
)
Population Of India
0
200
400
600
800
1000
1200
0 10 20 30 40
Year
Po
pu
lati
on
(M
illio
ns
)
Carrying CapacityCarrying Capacity
kt
kt
Ae+
M=M
Ae+
M=P
1
.00001
1
Year country will reach the carrying capacity:
U.S.A: 2543
Korea: 2305
Japan: 2150
India: 2543
Set P=M - .00001
Solve for t
ConclusionsConclusions
There are TOO many people in the world…..Thomas
Malthus was right….
Works CitedWorks Cited
http://www.library.uu.nl/wesp/populstat/Asia/skoreac.htm
http://geography.about.com/gi/dynamic/offsite.htm?zi=1/XJ&sdn=geography&zu=http%3A%2F%2Fwww.census.gov%2Fftp%2Fpub%2Fipc%2Fwww%2Fidbsum.html
http://www.library.uu.nl/wesp/populstat/Asia/japanc.htm
http://www.ugrad.math.ubc.ca/coursedoc/math100/notes/mordifeqs/logistic.html
http://en.wikipedia.org/wiki/Global_Population#Forecast_of_world_population
http://www.mnforsustain.org/united_states_population_growth_graph.htm
http://www.library.uu.nl/wesp/populstat/Asia/indiac.htm
http://www.cia.gov/cia/publications/factbook/geos/in.html#People
http://www.cia.gov/cia/publications/factbook/geos/us.html
http://www.cia.gov/cia/publications/factbook/geos/ja.html
http://www.cia.gov/cia/publications/factbook/geos/ks.html