A certain forest covers an area of 2000km squared . Suppose that each year this area decreases by 3.75% . What will the area be after 12 years?

To find the area of the forest after 12 years, given that it decreases by 3.75% each year, we can use the formula for exponential decay:

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

Where:
- \( A(t) \) is the area after \( t \) years.
- \( A_0 \) is the initial area.
- \( r \) is the rate of decrease.
- \( t \) is the number of years.

Given:
- \( A_0 = 2000 \) km²
- \( r = 3.75\% = 0.0375 \)
- \( t = 12 \) years

Now, let's calculate the area:

\[
A(12) = 2000 \times (1 - 0.0375)^{12}
\]

\[
A(12) = 2000 \times (0.9625)^{12}
\]

\[
A(12) \approx 2000 \times 0.64186
\]

\[
A(12) \approx 1283.72 \text{ km}^2
\]

So, the area of the forest after 12 years will be approximately **1283.72 km²**.

Would you like more details or have any other questions?

Here are 5 related questions:
1. How would the area change if the rate of decrease was 5% instead?
2. What would be the area after 20 years with the same rate of decrease?
3. How much area is lost in total after 12 years?
4. Can the forest area ever reach zero under this model? Why or why not?
5. What is the percentage decrease in area after 12 years compared to the initial area?

**Tip:** When dealing with exponential decay, small changes in the rate can significantly impact long-term outcomes.

Explore how to calculate the area of a forest after 12 years using exponential decay, with an initial area of 2000 km² decreasing by 3.75% annually. Learn the formula and steps involved in solving such decay problems. Suitable for Grades 9-12.

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