population growth of various countries
DESCRIPTION
Population Growth Of Various Countries. 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) - PowerPoint PPT PresentationTRANSCRIPT
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