In the beginning of B.S. 2015, the population of a town was 1,000,000 and the rate of population growth is [tex]2\%[/tex] every year. If 81,000 people migrated there from different places in the beginning of B.S. 2068, what will be the population of the town in the beginning of B.S. 2068?



Answer :

To find the population of the town in the beginning of BS 2068, we can break the problem down into a few steps:

1. Initial Population:
The initial population of the town in BS 2015 was 1,001,000.

2. Annual Growth Rate:
The population grows at a rate of 2% per year.

3. Number of Years:
We need to find the population at the beginning of BS 2068. This means we need to calculate the growth over a period from BS 2015 to BS 2068, which is:
[tex]\[ \text{Years} = 2068 - 2015 = 53 \text{ years} \][/tex]

4. Population Growth Calculation:
To find the population growth, we use the compound interest formula for population growth:
[tex]\[ \text{Population Growth} = \text{Initial Population} \times (1 + \text{Growth Rate})^{\text{Years}} \][/tex]
Given:
[tex]\[ \text{Initial Population} = 1,001,000 \][/tex]
[tex]\[ \text{Growth Rate} = 0.02 \text{ (or 2%)} \][/tex]
[tex]\[ \text{Years} = 53 \][/tex]
The population growth after 53 years is:
[tex]\[ \text{Population Growth} = 1,001,000 \times (1 + 0.02)^{53} \approx 2,859,191.08 \][/tex]

5. Migrated People:
At the beginning of BS 2068, 81,000 people migrated to the town. This migration increases the population accordingly.

6. Final Population Calculation:
The final population in BS 2068 is the sum of the population growth and the migrated people:
[tex]\[ \text{Final Population} = \text{Population Growth} + \text{Migrated People} \][/tex]
[tex]\[ = 2,859,191.08 + 81,000 \approx 2,940,191.08 \][/tex]

Therefore, the population of the town at the beginning of BS 2068 will be approximately 2,940,191.

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