A certain forest covers an area of $3400 \mathrm{~km}^{2}$. Suppose that each year this area decreases by $3.75 \%$. What will the area be after 8 years? Use the calculator provided and round your answer to the nearest square kilometer.

Step 1 ：The problem is asking for the area of the forest after 8 years given that it decreases by 3.75% each year. This is a problem of exponential decay. The formula for exponential decay is: \[ A = P(1 - r)^t \] where: \(A\) is the final amount remaining after the decay, \(P\) is the initial amount (the principal), \(r\) is the decay rate (in decimal form), and \(t\) is the time the money is invested or borrowed for, in years.

Step 2 ：In this case, \(P = 3400 \, \text{km}^2\), \(r = 3.75\% = 0.0375\), and \(t = 8 \, \text{years}\).

Step 3 ：We can substitute these values into the formula and calculate the final area.

Step 4 ：The calculated area of the forest after 8 years is approximately 2504.29 square kilometers. However, the problem asks for the answer to be rounded to the nearest square kilometer.

Step 5 ：Final Answer: The area of the forest after 8 years will be approximately \(\boxed{2504}\) square kilometers.