Answer :
To determine the population of the town after 3 years given the annual growth rates, let's follow these steps:
1. Initial Population: Start with the initial population which is 25,000.
2. First Year's Growth:
- Growth rate for the first year is 4%.
- To find the new population at the end of the first year, increase the initial population by 4%.
[tex]\[ \text{Population after 1st year} = 25000 \times (1 + 0.04) = 25000 \times 1.04 = 26000 \][/tex]
3. Second Year's Growth:
- Growth rate for the second year is 5%.
- To find the new population at the end of the second year, increase the population at the end of the first year by 5%.
[tex]\[ \text{Population after 2nd year} = 26000 \times (1 + 0.05) = 26000 \times 1.05 = 27300 \][/tex]
4. Third Year's Growth:
- Growth rate for the third year is 8%.
- To find the new population at the end of the third year, increase the population at the end of the second year by 8%.
[tex]\[ \text{Population after 3rd year} = 27300 \times (1 + 0.08) = 27300 \times 1.08 = 29484 \][/tex]
After calculating the population growth step-by-step for each year, we find that the population of the town after 3 years is 29,484.
Therefore, the correct answer is:
a. 29484
1. Initial Population: Start with the initial population which is 25,000.
2. First Year's Growth:
- Growth rate for the first year is 4%.
- To find the new population at the end of the first year, increase the initial population by 4%.
[tex]\[ \text{Population after 1st year} = 25000 \times (1 + 0.04) = 25000 \times 1.04 = 26000 \][/tex]
3. Second Year's Growth:
- Growth rate for the second year is 5%.
- To find the new population at the end of the second year, increase the population at the end of the first year by 5%.
[tex]\[ \text{Population after 2nd year} = 26000 \times (1 + 0.05) = 26000 \times 1.05 = 27300 \][/tex]
4. Third Year's Growth:
- Growth rate for the third year is 8%.
- To find the new population at the end of the third year, increase the population at the end of the second year by 8%.
[tex]\[ \text{Population after 3rd year} = 27300 \times (1 + 0.08) = 27300 \times 1.08 = 29484 \][/tex]
After calculating the population growth step-by-step for each year, we find that the population of the town after 3 years is 29,484.
Therefore, the correct answer is:
a. 29484
