Question

a certain forest covers an area of 3100 km². suppose that each year this area decreases by 3%. what will the area be after 6 years? use the calculator provided and round your answer to the nearest square kilometer.

Explanation:

Step1: Identify the formula for exponential decay

The formula for exponential decay is $A = A_0(1 - r)^t$, where $A_0$ is the initial amount, $r$ is the rate of decay as a decimal, and $t$ is the time in years. Here, $A_0=3100$, $r = 0.03$, and $t = 6$.

Step2: Substitute the values into the formula

$A=3100\times(1 - 0.03)^6=3100\times0.97^6$.

Step3: Calculate $0.97^6$

$0.97^6=0.97\times0.97\times0.97\times0.97\times0.97\times0.97\approx0.83374$.

Step4: Calculate the final area

$A = 3100\times0.83374\approx2584.594\approx2585$.

Answer:

2585