Certainly! Let's carefully solve the problem step by step.
1. Understand the problem: We start with a forest that initially covers an area of 3000 square kilometers (km²). Each year, this area decreases by 3%. We need to find out what the area of the forest will be after 11 years and round the final answer to the nearest square kilometer.
2. Know the formula: This situation can be modeled using a formula similar to that used for compound interest. When something decreases by a fixed percentage each year, the formula to find the remaining amount is:
[tex]\[
\text{Final Area} = \text{Initial Area} \times (1 - \text{Decrease Rate})^{\text{Number of Years}}
\][/tex]
3. Substitute the known values:
- Initial Area = 3000 km²
- Decrease Rate = 3% or 0.03
- Number of Years = 11
Substituting these values into the formula gives:
[tex]\[
\text{Final Area} = 3000 \times (1 - 0.03)^{11}
\][/tex]
4. Calculate the remaining percentage after each year:
[tex]\[
1 - 0.03 = 0.97
\][/tex]
5. Raise this remaining percentage to the power equal to the number of years:
[tex]\[
0.97^{11} \approx 0.715301
\][/tex]
6. Multiply the initial area by this result:
[tex]\[
\text{Final Area} = 3000 \times 0.715301 \approx 2145.904
\][/tex]
7. Round the final answer to the nearest square kilometer:
[tex]\[
\text{Final Area (rounded)} \approx 2146 \text{ km}^2
\][/tex]
Thus, the area of the forest after 11 years will be approximately 2146 square kilometers.
