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Population Forecasting Methods | Formulas | Example Problems | Practice Problem

Population forecasting is a method to predict/forecast the future population of an area. Usually, the population at the design period of water supply systems is predicted to find the water demand at that time, as the systems are required to fulfill their purposes till the end of the design period. Methods to predict the population are discussed further.


Arithmetical Increase or Arithmetical Mean Method


Where Arithmetical Increase Method is used


The arithmetical Increase Method is mainly adopted for old and developed towns, where the rate of population growth is nearly constant. Therefore, it is assumed that the rate of growth of the population is constant. It is similar to simple interest calculations. The population predicted by this method is the lowest of all.


Arithmetical Increase Method Derivation


dP/dt = K (say), where, dP/dt represents rate of growth of population.


Integrating the above equation over P1 to P2 over a time period of t1 to t2,

∫dP = K∫dt

[P2 - P1] = k * [t2 - t1]

P2 = P1 + K * Δt

P2 = P1 + x̄ * n

P2 = P1 + n


Arithmetical Increase Method Formula


Pn = Po + nx̄,

where,

Po - last known population

Pn - population (predicted) after 'n' number of decades,

n - number of decades between Po and Pn and,

x̄ - the rate of population growth.


Arithmetical Increase Method Example Problem


The following data (common data) will be used in the example problems for all other methods to be discussed.

Year

Population

1930

25000

1940

28000

1950

34000

1960

42000

1970

47000

Question: With the help of the common data find the population for the year 2020 using the arithmetic increase method.

Solution:

Step 1: Find the increase in population each decade.

Year

Population

Increase

1930

25000

-

1940

28000

3000

1950

34000

6000

1960

42000

8000

1970

47000

5000

Step 2: Find the average rate of increase of population (x̄)

x̄ = (3000+6000+8000+5000)/4

x̄ = 22000/4

x̄ = 5500


Step 3: Find the number of decades (n) between the last known year and the required year

n = 5 (5 decades elapsed between 1970 and 2020)


Step 4: Apply the formula Pn = Po + nx̄,

P[2020] = P[1970] + (5 * 5500)

P[2020] = 47000 + 27500

P[2020] = 74,500. Therefore, population at 2020 will be 74,500.


Geometrical Increase Method


Where Geometrical Increase Method is used


This method is adopted for young and developing towns, where the