Question

incorrect
your answer is incorrect.
a certain forest covers an area of 2700 km². suppose that each year this area decreases by 9%. what will the area be after 11 years?
use the calculator provided and round your answer to the nearest square kilometer.
□ km²

Explanation:

Step1: Identify the formula for exponential decay

The formula for exponential decay is \( A = P(1 - r)^t \), where \( A \) is the final amount, \( P \) is the initial amount, \( r \) is the rate of decay (as a decimal), and \( t \) is the time in years.
Here, \( P = 2700 \), \( r = 0.09 \) (since 9% = 0.09), and \( t = 11 \).

Step2: Substitute the values into the formula

Substitute \( P = 2700 \), \( r = 0.09 \), and \( t = 11 \) into the formula:
\( A = 2700(1 - 0.09)^{11} \)
First, calculate \( 1 - 0.09 = 0.91 \).
Then, calculate \( 0.91^{11} \). Using a calculator, \( 0.91^{11} \approx 0.3503 \).

Step3: Calculate the final area

Multiply \( 2700 \) by \( 0.3503 \):
\( A = 2700 \times 0.3503 \approx 945.81 \)
Rounding to the nearest square kilometer, we get \( 946 \).

Answer:

\( 946 \)