A town has a population of 176400, which increases at a rate of 5% annually. What will be the population after two years?

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Points to Remember:

  • Compound annual growth rate (CAGR) calculation.
  • Application of the formula for exponential growth.
  • Understanding the concept of population growth.

Introduction:

This question requires a factual and analytical approach to determine the future population of a town given its current size and annual growth rate. Population growth is a crucial demographic factor influencing resource allocation, infrastructure planning, and economic development. Understanding population projections is essential for effective urban planning and policy-making. This problem involves calculating compound growth, where the growth each year is added to the base population before calculating the next year’s growth.

Body:

Understanding Compound Annual Growth Rate (CAGR):

Population growth, in this case, follows a compound annual growth rate (CAGR) model. Unlike simple interest, where growth is calculated only on the principal amount, CAGR calculates growth on the principal amount plus accumulated growth from previous periods. This means the population increase each year is larger than the previous year.

Calculating the Population After Two Years:

We can use the following formula to calculate the population after two years:

Future Population = Present Population * (1 + Growth Rate)^Number of Years

Where:

  • Present Population = 176400
  • Growth Rate = 5% = 0.05
  • Number of Years = 2

Substituting the values into the formula:

Future Population = 176400 * (1 + 0.05)²
Future Population = 176400 * (1.05)²
Future Population = 176400 * 1.1025
Future Population = 194415

Therefore, the population of the town after two years will be 194,415.

Limitations and Considerations:

This calculation assumes a constant growth rate of 5% annually. In reality, population growth is influenced by various factors such as birth rates, death rates, migration patterns, and unforeseen events (e.g., epidemics, natural disasters). The 5% growth rate might not remain constant over the two years. A more sophisticated model incorporating these factors would provide a more accurate projection.

Conclusion:

Using the compound annual growth rate formula, we have determined that the population of the town will be approximately 194,415 after two years, assuming a constant 5% annual growth rate. It’s crucial to remember that this is a simplified model, and real-world population growth is far more complex. For more accurate projections, incorporating factors like birth rates, death rates, and migration patterns into a more comprehensive model is necessary. Effective urban planning requires accurate population projections to ensure sustainable development and resource allocation, aligning with the principles of holistic development and responsible governance.

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