Points to Remember:
- Annual population growth rate: 10%
- Current population: 20,000
- Calculation period: 2 years
- Compound growth calculation required.
Introduction:
This question requires a factual and analytical approach to determine the future population of a city given a constant annual growth rate. Population growth is a crucial demographic indicator, influencing urban planning, resource allocation, and economic development. Understanding population dynamics allows for better forecasting and resource management. This problem involves a compound growth calculation, where the growth each year is added to the previous year’s total population before calculating the next year’s growth.
Body:
Calculating Population Growth:
The population growth is compounded annually. This means that the 10% increase in year one becomes part of the base population for year two’s calculation. We can calculate this in two ways:
Method 1: Step-by-Step Calculation
- Year 1: 20,000 + (10% of 20,000) = 20,000 + 2,000 = 22,000
- Year 2: 22,000 + (10% of 22,000) = 22,000 + 2,200 = 24,200
Therefore, the population after two years will be 24,200.
Method 2: Compound Interest Formula
A more efficient method uses the compound interest formula:
Future Population (FP) = Present Population (PP) * (1 + growth rate)^number of years
FP = 20,000 * (1 + 0.10)²
FP = 20,000 * (1.1)²
FP = 20,000 * 1.21
FP = 24,200
Again, the population after two years will be 24,200.
Limitations of the Model:
This calculation assumes a constant 10% annual growth rate. In reality, population growth is influenced by various factors such as birth rates, death rates, migration patterns, and economic conditions. These factors can fluctuate significantly, making a constant growth rate an oversimplification. The model also doesn’t account for potential events like natural disasters or epidemics that could drastically alter the population.
Conclusion:
Using both a step-by-step approach and the compound interest formula, we determine that the city’s population will be 24,200 after two years, assuming a constant 10% annual growth rate. It’s crucial to remember that this is a simplified model. For more accurate predictions, a more sophisticated model incorporating various demographic and socio-economic factors should be employed. Effective urban planning requires considering these complexities and developing strategies for sustainable and inclusive growth, ensuring the well-being of the city’s inhabitants. Further research into the specific factors influencing the city’s population growth would provide a more nuanced and accurate projection.
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