Population forecasting – geometrical increase method A city has a population of 50,000 in the year 2000. The average percentage increase per decade from records is 20%. Using the geometrical increase method, estimate the population in the year 2020.

Introduction / Context:
Population forecasting informs capacity planning for water supply, wastewater, and urban infrastructure. The geometrical (compound) increase method assumes population grows by a constant percentage over equal time intervals.

Given Data / Assumptions:

• Base population P0 = 50,000 at year 2000.
• Average percentage increase per decade r = 20% = 0.20.
• Forecast year = 2020 → two decades ahead (n = 2).

Concept / Approach:
Geometrical increase method uses compound growth: Pn = P0 * (1 + r)^n. Here, n is the number of decades between base and forecast years.

Step-by-Step Solution:
Identify n = 2 decades (2000 → 2010 → 2020).Compute growth factor: (1 + 0.20)^2 = 1.2^2 = 1.44.Forecast population: P2020 = 50,000 * 1.44 = 72,000.

Verification / Alternative check:
Check intermediate decade: 2000→2010 = 50,000 * 1.2 = 60,000; 2010→2020 = 60,000 * 1.2 = 72,000. Matches direct computation.

Why Other Options Are Wrong:

• 56,000; 60,000; 64,000; 70,000 correspond to lower effective growth rates or arithmetic increases, not the specified 20% compound per decade.

Common Pitfalls:
Applying arithmetic increase instead of geometric; using 20% per year instead of per decade; forgetting to square the factor for two decades.

Final Answer:
72,000