Population Calculation After Percentage Changes
This problem requires calculating the final population after a series of percentage changes over three years, starting from an initial population.
Initial Population Value
The starting population of the town is given as 50,000.
Yearly Population Changes
The population dynamics over the three years are as follows:
- Year 1: Population increased by 25%.
- Year 2: Population decreased by 20%.
- Year 3: Population increased by 10%.
Step-by-Step Population Calculation
We calculate the population at the end of each year sequentially:
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End of Year 1: The population increases by 25%.
The calculation is: \(P_1 = 50,000 \times (1 + \frac{25}{100}) = 50,000 \times (1 + 0.25) = 50,000 \times 1.25 = 62,500\)
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End of Year 2: The population decreases by 20% from the Year 1 value.
The calculation is: \(P_2 = 62,500 \times (1 - \frac{20}{100}) = 62,500 \times (1 - 0.20) = 62,500 \times 0.80 = 50,000\)
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End of Year 3: The population increases by 10% from the Year 2 value.
The calculation is: \(P_3 = 50,000 \times (1 + \frac{10}{100}) = 50,000 \times (1 + 0.10) = 50,000 \times 1.10 = 55,000\)
Combined Percentage Change Calculation
Alternatively, the final population can be found using a single combined calculation:
Final Population = Initial Population \(\times (1 + \text{Rate}_1) \times (1 - \text{Rate}_2) \times (1 + \text{Rate}_3)\)
Final Population = \(50,000 \times (1 + 0.25) \times (1 - 0.20) \times (1 + 0.10)\)
Final Population = \(50,000 \times 1.25 \times 0.80 \times 1.10\)
Final Population = \(50,000 \times (1) \times 1.10 = 55,000\)
Conclusion on Population After 3 Years
The population of the town after 3 years is 55,000.
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