To determine the area of the forest after 8 years, we need to account for the annual decrease of 7%. This can be calculated using the formula for exponential decay:

$$ A = P \times (1 - r)^t $$

where:
- $ A $ is the area after $ t $ years,
- $ P $ is the initial area,
- $ r $ is the rate of decrease,
- $ t $ is the number of years.

Given:
- $ P = 3900 $ km²,
- $ r = 0.07 $,
- $ t = 8 $ years.

Substitute these values into the formula:

$$ A = 3900 \times (1 - 0.07)^8 $$

First, calculate $ 1 - 0.07 $:

$$ 1 - 0.07 = 0.93 $$

Next, raise 0.93 to the power of 8:

$$ 0.93^8 \approx 0.582 $$

Now, multiply this result by the initial area:

$$ A = 3900 \times 0.582 \approx 2269.8 $$

Rounding to the nearest square kilometer:

$$ A \approx 2270 \text{ km}^2 $$

Therefore, the area of the forest after 8 years will be approximately 2270 square kilometers.

Question

To determine the area of the forest after 8 years, we need to account for the annual decrease of 7%. This can be calculated using the formula for exponential decay:

$$ A = P \times (1 - r)^t $$

where:
- $ A $ is the area after $ t $ years,
- $ P $ is the initial area,
- $ r $ is the rate of decrease,
- $ t $ is the number of years.

Given:
- $ P = 3900 $ km²,
- $ r = 0.07 $,
- $ t = 8 $ years.

Substitute these values into the formula:

$$ A = 3900 \times (1 - 0.07)^8 $$

First, calculate $ 1 - 0.07 $:

$$ 1 - 0.07 = 0.93 $$

Next, raise 0.93 to the power of 8:

$$ 0.93^8 \approx 0.582 $$

Now, multiply this result by the initial area:

$$ A = 3900 \times 0.582 \approx 2269.8 $$

Rounding to the nearest square kilometer:

$$ A \approx 2270 \text{ km}^2 $$

Therefore, the area of the forest after 8 years will be approximately 2270 square kilometers.

Knowee AI · Accepted Answer