A certain forest covers an area of 5000 km^2. Suppose that each year this area decreases by 3.25%. What will the area be after 7 years?

To find the area of the forest after 7 years, 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 (as a decimal),
- \( t \) is the number of years.

Given:
- Initial area \( A_0 = 5000 \, \text{km}^2 \),
- Rate of decrease \( r = 3.25\% = 0.0325 \),
- Time \( t = 7 \) years.

Plugging the values into the formula:

\[
A(7) = 5000 \times (1 - 0.0325)^7
\]

\[
A(7) = 5000 \times (0.9675)^7
\]

Now, let's calculate this value.

\[
A(7) \approx 5000 \times 0.7967 = 3983.5 \, \text{km}^2
\]

So, the area of the forest after 7 years will be approximately **3983.5 km²**.

Would you like more details on this calculation, or do you have any other questions?

Here are five related questions:
1. How would the area change if the rate of decrease was 5% instead of 3.25%?
2. What will the area be after 10 years with the same rate of decrease?
3. How long will it take for the area to be reduced to half its original size?
4. What would be the formula if the decrease were happening monthly instead of annually?
5. If the forest area is increasing instead of decreasing by 3.25% annually, what will the area be after 7 years?

**Tip:** When dealing with exponential decay problems, always convert the percentage rate into a decimal before applying the formula.

Explore how to calculate the area of a forest over time as it decreases annually by 3.25%. Use our step-by-step solution to find the area after 7 years. Suitable for high school students studying exponential decay and percentage calculations.

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