Exponential and Logarithmic Functions
Finding a final amount in a word problem on exponential growth or decay
Kayleigh
A certain forest covers an area of $1800 \mathrm{~km}^{2}$. Suppose that each year this area decreases by $4.5 \%$. What will the area be after 12 years?
Español
Use the calculator provided and round your answer to the nearest square kilometer.
\[
\prod \mathrm{km}^{2}
\]
\[
\times
\]
ऽ

Step 1 ：A certain forest covers an area of 1800 square kilometers. Suppose that each year this area decreases by 4.5%. We are asked to find the area of the forest after 12 years.

Step 2 ：We can use the formula for exponential decay to solve this problem. The formula is \(A = P(1 - r)^t\), where \(A\) is the final amount, \(P\) is the initial amount, \(r\) is the rate of decay, and \(t\) is the time.

Step 3 ：Substituting the given values into the formula, we get \(A = 1800(1 - 0.045)^{12}\).

Step 4 ：Calculating the above expression, we find that \(A \approx 1035.888386386458\).

Step 5 ：Rounding to the nearest square kilometer, we get \(A \approx 1036\).

Step 6 ：Final Answer: The area of the forest after 12 years will be approximately \(\boxed{1036}\) square kilometers.