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Incremental increase method
• Population varies at a progressive rate and not at
a constant rate.
• This method includes the benefits of the both
previous methods:
- Average increase per decade is found out
- Incremental increase or decrease in the
population change for each decade is found out
- Average incremental increase is worked out
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Incremental increase method
• Mathematically, population at the end of n decade is
estimated as:
Pn =
P + n . d + (1 + 2 + 3 + …..n) . t
Pn =
P + n . d + [n(n + 1)/2] . t
Where,
Pn
P =
d
t =
= Future population after ‘n’ decades;
Present population;
= average increase per decade;
average incremental increase.
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Example
Ex.2: Find the population for 2030 for a design period
of 30 years using incremental increase method.
Census is available from the year 1960 to 2000,
given below:
Year
Population
1960
35,000
1970
37,500
1980
43,500
1990
52,000
2000
57,500
Answers:
80,375
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Solution to Ex.2
Year
Population
Increase in
population
Incremental
increase
1960
35,000
-
-
1970
37,500
2500
-
1980
43,500
6000
+ 3500
1990
52,000
8500
+ 2500
2000
57,500
5500
- 3000
SUM
22500
3000
Average
22500/4 =
5625
3000/3 = 1000
Pn
=
P + n . d + [n(n + 1)/2] . t
Pn
=
57500 + 3 x 5625 + [3(3 + 1)/2] x 1000
Pn
=
80,375
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Logistic growth method
• Most scientific way of forecasting population.
• The population is projected for future years
with a sigmoid curve (S-curve), logistic
growth curve.
• Because growth rates (as in other methods)
cannot continue steadily and for long time –
some environmental constraints limit
further growth.
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• In geometrical increase method,
population increases exponentially.
• If this increase continues, one day the
system will not able to accommodate
and sustain such increase.
• As a result, there will be some
decrease in growth – which is not
taken care by exponential growth.
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• The rate of increase of population with
time increases initially
• Later it starts decreasing
• Reason - mainly due to the
crowding effect and resources
crunch in the system.
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Mathematical expressions
Growth rate increasing exponentially:
Solution:
Growth rate decreasing:
Solution:
91
…contd
By introducing r0 as an initial growth rate
Equate both and solve for r
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Example
• Ex. 3: find the population for the year 2040 using
logistic growth method when the population in the city
in 2000 is 5 lakhs and a growth rate of 1.6%. Assume
K = 20 lakhs.
Solution:
The rate of population growth, r = 0.0213
The population in 2040, N = 8.77 lakhs
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