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.