Question

A certain forest covers an area of 1800 km^2. Suppose that each year this area decreases by 6.25%. What will
the area be after 8 years?
Use the calculator provided and round your answer to the nearest square kilometer.

Answer 1

To calculate the area of the forest after 8 years with an annual decrease of 6.25%, we can use the formula for exponential decay:

\[
A = A_0 (1 - r)^t
\]

where:
- \( A \) is the area after \( t \) years,
- \( A_0 \) is the initial area (in this case, 1800 km²),
- \( r \) is the rate of decrease (6.25% or 0.0625),
- \( t \) is the number of years (8).

Plugging in the values:

\[
A = 1800 \times (1 - 0.0625)^8
\]
\[
A = 1800 \times (0.9375)^8
\]

Now calculating \( (0.9375)^8 \):

\[
(0.9375)^8 \approx 0.527
\]

Now substituting back into the equation:

\[
A \approx 1800 \times 0.527 \approx 948.6
\]

Rounding to the nearest square kilometer, the area after 8 years will be approximately:

\[
\boxed{949} \text{ km}^2
\]