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Modelling and Simulation Challenge In-Class Written Mock Exam 2

The document discusses world population growth rates and estimates. It provides two modeling challenges: 1) Develop a system dynamics model to determine doubling times for peak (2.2%) and current (1.1%) growth rates, and estimate the population by 2040. The doubling times are 21 years for 2.2% and 63 years for 1.1%. 2) Develop a model disaggregating births and deaths, using information that annual births were 134 million in 2011 and deaths are estimated to reach 80 million by 2040. This model estimates the 2040 population will be 8.96 billion.

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Nikhil Mitra
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30 views3 pages

Modelling and Simulation Challenge In-Class Written Mock Exam 2

The document discusses world population growth rates and estimates. It provides two modeling challenges: 1) Develop a system dynamics model to determine doubling times for peak (2.2%) and current (1.1%) growth rates, and estimate the population by 2040. The doubling times are 21 years for 2.2% and 63 years for 1.1%. 2) Develop a model disaggregating births and deaths, using information that annual births were 134 million in 2011 and deaths are estimated to reach 80 million by 2040. This model estimates the 2040 population will be 8.96 billion.

Uploaded by

Nikhil Mitra
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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You are on page 1/ 3

Prof. Dr.

Jrgen Strohhecker

Modelling and Simulation Challenge


In-class Written Mock Exam 2
The world population is the total number of living humans on Earth. As of July
2013, it is estimated to number 7.151 billion by the United States Census Bureau
(USCB). The USCB estimates that the world population exceeded 7 billion on
March 12, 2012,
The world population has continuously grown since the end of the Great Famine
and the Black Death in 1350, when it was near 370 million. The fastest growth
rates global population increases above 1.8% per year occurred briefly during
the 1950s, and for longer during the 1960s and 1970s. The global growth rate
peaked at 2.2% in 1963, and has declined to below 1.1% as of 2012. Total
annual births were highest in the late 1980s at about 138 million, and are now
expected to remain essentially constant at their 2011 level of 134 million, while
deaths number 56 million per year, and are expected to increase to 80 million per
year by 2040. (Source: http://en.wikipedia.org/wiki/World_population)

1) Develop a system dynamics world population model for the purpose of


determining the doubling time for the peak (2.2% per year) and current (1.1%
per year) growth rates. (Please note, that in system dynamics terminology
these growth rates should be named fractional net population growth rates.)
Determine the doubling times via simulation and the population by 2040.
2) Develop a second system dynamics world population model that
disaggregates the net flow and uses the information on births and deaths
provided in the Wikipedia excerpt. Which population can be expected by
2040? (Use the limited information provided above as reasonable as
possible.)

Page 1

Prof. Dr. Jrgen Strohhecker

Solution
1)

Population Net
Change

Population

IV Population
fractional net
population growth rates

FINAL TIME = 2100


Units: Year
INITIAL TIME = 2012
Units: Year
SAVEPER = TIME STEP
Units: Year
TIME STEP = 0.125
Units: Year
fractional net population growth rates = 0.022
Units: 1/Year
IV Population = 7000
Units: M persons
Population = INTEG( Population Net Change , IV Population )
Units: M persons
Population Net Change = Population * fractional net population growth rates
Units: M persons/Year
Answer:
Doubling Time 2.2 % Growth Rate: 21 Jahre
Doubling Time 1.1 % Growth Rate: 63 Jahre

Page 2

Prof. Dr. Jrgen Strohhecker

2)
Population
Deaths

Births
IV Population

fractional death rate

2011 Deaths

Equations:
FINAL TIME = 2040
Units: Year
INITIAL TIME = 2012
Units: Year
SAVEPER = TIME STEP
Units: Year
TIME STEP = 0.125
Units: Year
"2011 Deaths" = 56
Units: M persons/Year
Births = 134
Units: M persons/Year
Deaths = Population * fractional death rate
Units: M persons/Year
fractional death rate = "2011 Deaths" / IV Population
Units: 1/Year
IV Population = 7000
Units: M persons
Population = INTEG( Births - Deaths , IV Population )
Units: M persons
Answer:
Population in 2040: 8960 M persons

Page 3

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