Population Forecasting using
Geometric Increase Method
Presented by:
Bhantooa Luvindraj (1014582)
Boyjoo Manoj (1014504)
Bundhoo Deepshika (1017841)
Ramgoolam Oomeshnathsingh (1019085)
Seburn Indra (1015380)
Population Forecasting
Population Forecasting consists of mathematical models which are
used to analyse changes in population numbers.
There are several factors affecting changes in population:
 Increase due to births
 Decrease due to deaths
 Increase/Decrease due to migration
 Increase due to annexation
All the above data can be obtained from the census population records.
In Mauritius, these information can be obtained at the Central
Statistics Office (CSO)
…Population Forecasting
The various mathematical methods available are generally classified in
two categories: Short term methods and Long term methods
Short term methods (1-10 years)
 Arithmetic progression
 Geometric progression
 Incremental increase method
 Decreasing rate of growth
 Simple graphical method
Long term methods (10-50 years)
 Comparative graphical method
 Ratio method
 Logistic curve method
Why is population forecasting important?
 Population forecasting is an integral part of design. It is essential to take into account
the population at the end of the design period.
 Fundamental to planning
(Assumptions and estimates used in determining sewage flow have a permanent
effect on planning decisions and outcomes)
 Premature and excessive investments in works
 System failure and hence increasing customer complaints
 Environmental impact
 Essential to service provider so as to know the spare capacity of the system
 Identification of weak links of system
Ability to accept new/unexpected demands
When can projections be carried out?
Projections are likely to be carried out for the design of a
system. A service provider should have knowledge of current
demand/flow and anticipated future projections at all times.
Projections should be determined:
 Once the needs of the service are already known and the
objectives determined
 Stakeholder requirements have been identified
 Adequate raw data on existing flows/demands is available
Geometric Increase Method
The basic model for geometric change in population size is:
P = P o λt
which is based on the hypothesis that rate of change of population is
proportional to the population. According to this, method it is assumed that the
rate of increase of population growth in a community is proportional to the
present population.




Po denotes initial size,
P denotes population at time t
t denotes time (measured in decades)
λ is the ‘finite population multiplier’ which can be interpreted as λ = ℮i
for continuous change or λ = 1+ i for discrete (constant) ‘compound
interest’ or ‘birth-pulse’ populations.
Example
Predict the population for the years 2023, 2033, and 2043
from the following census figures of a town using
geometric method.
Year
Population:
(thousands)
1943 1953
60
65
1963 1973 1983 1993
63
72
79
89
2003
2013
97
120
Solution
1. USING DISCRETE METHOD (RATE OF CHANGE IS
CONSTANT)







P = Poλt
λ = (1+ i) for discrete change
Therefore P = Po (1+i)t where,
P0 : Initial population size
P: Population size at time t
i: Average percentage increase per decade
t: Number of decades
…Solution (using discrete method)
Year
1943
Population:
(thousands)
60
Increment
per Decade
-
Percentage Increment
per Decade
-
1953
65
+5
(5÷60) x 100 = +8.33
1963
63
-2
(2÷65) x 100 = -3.07
1973
72
+9
(9÷63) x 100 = +14.28
1983
79
+7
(7÷72) x 100 = +9.72
1993
89
+10
(10÷79) x 100 = +12.66
2003
97
+8
(8÷89) x 100 = +8.98
2013
120
+23
(23÷97) x 100 = +23.71
Net values
-
+60
+74.61
Averages
-
8.57
10.66
…Solution (using discrete method)Solution
 Population for 2023 = Population 2013 x (1+i/100) t
= 120 x (1+10.66/100), where i = 10.66, t = 1
= 120 x 110.66/100 = 132.8
 Population for 2033 = Population 2013 x (1+i/100) t
= 120 x (1+10.66/100)2, where i = 10.66, t = 2
= 120 x 1.2245 = 146.95
 Population for 2043 = Population 2013 x (1+i/100) t
= 120 x (1+10.66/100)3, where i = 10.66, t = 3
= 120 x 1.355 = 162.60
2. CONTINOUS METHOD (RATE OF
CHANGE IS INCREASING)






𝑑𝑃
=𝑖
𝑃
𝑑𝑃
=
𝑃
. 𝑑𝑡
𝑖 . 𝑑𝑡
ln 𝑃 = 𝑖𝑡 + 𝑐
(When t = 0, P = Po, therefore c = ln Po)
ln 𝑃 = 𝑖𝑡 + ln 𝑃𝑜
ln 𝑃 − ln 𝑃𝑜 = 𝑖𝑡
 ( ln 𝑃 − ln 𝑃𝑜 =

ln 𝑃
ln 𝑃𝑜

𝑃
𝑃𝑜
= 𝑖𝑡
= 𝑒 𝑖𝑡
 𝑃 = 𝑃𝑜 𝑒 𝑖𝑡
ln 𝑃
ln 𝑃𝑜
)
…Solution (using continuous method)






P = Poλt
λ = ℮ i for continuous change
P0 : Initial population size
P: Population size at time t
i: Average percentage increase per decade
t: Number of decades
 The average rate of increase ‘i’ is calculated in the same
way as for the discrete change.
…Solution (using continuous method)
 Population for 2023 = Population 2013 x e it
= 120 x e(10.66/100 *1), where i = 10.66, t = 1
= 133.50
 Population for 2033 = Population 2013 x eit
=120 x e(10.66/100 *2), where i = 10.66, t = 2
=148.52
 Population for 2043 = Population 2013 x e it
=120 x e(10.66/100 *3), where i = 10.66, t = 3
= 165.22
…solution (comparison of results)
Year
Forecasted Population
Discrete Method
Continuous Method
2023
132.80
133.50
2033
146.95
148.52
2043
162.60
165.22
…solution (comparison of results)
Geometric Progression Curve
180
160
140
120
100
80
60
40
1940
1960
1980
Discrete Method
2000
2020
Continuous Method
2040
2060
…solution (comparison of results)
Geometric Progression curve
170
165
160
155
150
145
140
135
130
2020
2025
2030
Discrete Method
2035
Continuous Method
2040
2045
…solution (comparison of results)
 In the graph, we can conclude that values obtained from
the continuous method are higher than those obtained
from the discrete method. This is because in the discrete
method, the rate of increase of population is constant
whereas the continuous method has an increasing rate of
increase of population.
 In order to calculate the population number for any other
specific year within the decade, the same graph can be
used.
Advantages of Geometric Progression




Geometric extrapolation is desirable for short intervals
Simple method
When forecasting for a new city
Geometric rates are preferable to arithmetic rates for the
extrapolation of decreases in population over a series of
years
Limitations of Geometric Progression
 When the geometric rate of increase is high and the
period of time is long
 If the accuracy of the basic census figures is subject to
considerable doubt
 Where the death rate is declining while the birth rate
remains nearly constant
Population Forecasting in the Design of Waste
Water system
 Quantity of sewage at the end of a design period
= Per capita production of sewage x Forecasted
population at the end of the design period
 The quantity of wastewater generated per capita is
estimated to be 80% of the water consumption per
capita.
 The water consumption per occupant per day, for
different institutions, can be obtained from the table
…Population Forecasting in the Design of
Waste Water system
Conclusion
 In the light of the above, we can see that the Geometric
Increase Method is a simple realistic population model
based on past information. This method tends to give a
higher estimate than normal since it behaves
exponentially. It more accurately describes the
continuous and cumulative nature of population growth.
In normal practice, an average of the arithmetic method
and geometric method is performed to get a more
accurate estimate.
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