Geometric Increase Method of Population Forecasting (Uniform Percentage Growth Method)

Geometric increase method of population forecasting is also known as:

• Geometric progression method
• Uniform percentage growth method
• Uniform increase method

Geometric Increase Method Concept

Geometric increase method of population forecasting considers the percentage increase per decade. Geometrical increase method gives high results as percent decreases when the city grows towards saturation. While the arithmetic increase method gave low results as percent always remained constant.

This method of population forecast is analogous to compound interest calculations. Here, the growth rate per decade (r) is analogous to interest rate per annum of compound interest calculations.

Assumption used in geometric increase method:

“The percentage growth rate from decade to decade is constant.”

In other words, if the population increases by 10% in the past decade, then the population increase in the following decade will also be by 10%.

Owing to the fact that growth rate is considered constant, geometric increase method is also called uniform increase method.

Where Geometric Increase Method is Used?

Geometric increase method of population forecasting is suitable for towns where growth rate of population is proportional to the present population.

Geometric increase method is more applicable in city or towns which are in developing phase.

Geometric Increase Method Formula                                                 

P₁ = Population (predicted) after a decade from the last known population

P₀ = last known population

r = average of rate of population growth per decade

Similarly, to calculate population after n number of decades, following formula should be used –

P₀ = population at the end of last known decade

n = number of decades between last known population decade and decade at which population is to be predicted

P_n = population estimated after n number of decades 

Merits of Geometric Increase Method of Population Forecasting

• It can be applied to estimate the population of developing towns and cities.
• It can be applied to the cities having growth rate of population proportional to the present population.

Steps to do Geometrical Increase Method

1. Find increment in population in each decade from the census data of the past 3-4 decades.
2. Calculate growth rate of each decade (r) by the formula – r = increment in population/original population * 100
3. Find average of the growth rate over all the decades to find the value of r.
4. Now, fill in the values in the above formula to calculate the population.

Geometric Increase Method Problems/Example

Find the population of Delhi, India for the year 2021 from the population census data:

Year	1971	1981	1991	2001	2011
Population	40,65,698	62,20,406	94,20,644	1,38,50,507	1,67,87,941

Step-1: Given Data-

Population of last decade (2001) P = 1,38,50,507

Number of decades n = 2011-2001/10 = 1

Step-2: Find average percent increase per decade = r

Year	Population	Increment per Decade	% Increment per Decade
1971	40,65,698	–	–
1981	62,20,406	21,54,708	21/40 * 100 = 53%
1991	94,20,644	32,00,238	51.45%
2001	1,38,50,507	44,29,863	47.02%
2011	1,67,87,941	29,37,434	21.21%
Average increase per decade =		1,27,22,243/4 =31,80,560.75 = 31,80,561	172.68/4 =43.17%

Step-3: Calculate Pn from the formula

Pn = P0 [1+r/100]n

P2011= 1,67,87,941 [1+43.17/100]1

= 1,67,87,941 + (1)( 31,80,561)

= 1,99,68,502

Difference between Arithmetic Increase Method and Geometrical increase Method

SR No	Arithmetical Increase Method	Geometrical Increase Method
1	Population growth is assumed constant	Percentage rate of population growth is assumed constant
2	No compounding is done while estimating the population	Compounding is done at the end of every decade while estimating the population
3	Computation is analogous to simple interest calculations	Computation is analogous to compound interest calculations

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