a certain forest covers an area of 2200 km². suppose that each year this area decreases by 7.5%. what will…

a certain forest covers an area of 2200 km². suppose that each year this area decreases by 7.5%. what will the area be after 13 years? use the calculator provided and round your answer to the nearest square kilometer.

a certain forest covers an area of 2200 km². suppose that each year this area decreases by 7.5%. what will the area be after 13 years? use the calculator provided and round your answer to the nearest square kilometer.

Answer

Explanation:

Step1: Use the formula for exponential decay

The formula for exponential decay is (A = P(1 - r)^t), where (P) is the initial amount, (r) is the rate of decay (as a decimal), and (t) is the time. Here, (P = 2200), (r=0.075), and (t = 13).

Step2: Substitute the values into the formula

[ \begin{align*} A&=2200\times(1 - 0.075)^{13}\ &=2200\times(0.925)^{13} \end{align*} ]

Step3: Calculate ((0.925)^{13})

Using a calculator, ((0.925)^{13}\approx0.3777)

Step4: Calculate (A)

[ \begin{align*} A&=2200\times0.3777\ &=830.94\approx831 \end{align*} ]

Answer:

(831)