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.
