Arithmetic, Geometrical, and Decadal Population Growth methods, including formulas and their interpretation. These are widely used techniques in demography and urban planning to estimate or analyze population growth trends.
1. Arithmetic Growth Method
✅ Definition:
The Arithmetic growth method assumes that the population increases by a constant number of people every year. This method is suitable for short-term projections and when population growth is linear or slow.
✅ Formula:
Where:
PtP_tPt = Projected population at time ttt
P0P_0P0 = Base year population
rrr = Average annual increase in population
ttt = Number of years from base year
✅ How to calculate r:
If data from two known years is available: r=Pn−P0nr = \frac{P_n – P_0}{n}r=nPn−P0
Where:
PnP_nPn = Population at the end of nnn years
P0P_0P0 = Initial population
nnn = Number of years between the two known populations
✅ Example:
Population in 2000 = 50,000
Population in 2010 = 60,000
r=(60,000−50,000)/10=1,000r = (60,000 – 50,000)/10 = 1,000r=(60,000−50,000)/10=1,000 people/year
So, for 2015: P2015=50,000+(1,000×15)=65,000P_{2015} = 50,000 + (1,000 \times 15) = 65,000P2015=50,000+(1,000×15)=65,000
2. Geometric Growth Method
✅ Definition:
In the Geometric growth method, the population increases at a constant rate (percentage) every year. Each year’s increase is compounded on the previous year’s population. It follows exponential growth.
✅ Formula:
Where:
PtP_tPt = Projected population at time ttt
P0P_0P0 = Base year population
rrr = Annual growth rate (expressed as a decimal, e.g., 2% = 0.02)
ttt = Number of years
✅ How to calculate rrr:
r=(PnP0)1n−1r = \left(\frac{P_n}{P_0}\right)^{\frac{1}{n}} – 1r=(P0Pn)n1−1
Where:
PnP_nPn = Population at year nnn
P0P_0P0 = Population at base year
nnn = Number of years
✅ Example:
3. Decadal Growth Method
✅ Definition:
The Decadal Growth Method calculates the percentage increase in population over a 10-year (decade) period. It’s commonly used in census analysis to measure long-term growth trends.
✅ Formula:
Where:
P0P_0P0 = Population at the start of the decade
PnP_nPn = Population at the end of the decade
✅ Average Annual Growth Rate:
Annual Growth Rate (%)=Decadal Growth Rate10\text{Annual Growth Rate (\%)} = \frac{\text{Decadal Growth Rate}}{10}Annual Growth Rate (%)=10Decadal Growth Rate
Alternatively, Compounded Decadal Growth Rate (CDGR) can also be used: r=
✅ Example:
✅ Summary Table:
✅ Application in Urban Planning and Demography:
Arithmetic: Small towns, rural settlements, or areas with stable growth
Geometric: Rapidly urbanizing regions, metropolitan cities
Decadal: Used by national census authorities to compare growth between decades
