This question involves calculating the area of a forest after 13 years when the area decreases annually by 8.75%. This is a problem of exponential decay.

The formula for exponential decay is:
$A = A_0 \times (1 - r)^t$ Where:

• $A_0$ = Initial area ($5000 \, \text{km}^2$)
• $r$ = Annual rate of decrease ($0.0875$)
• $t$ = Time in years ($13$)
• $A$ = Area after 13 years

Let's calculate:
$A = 5000 \times (1 - 0.0875)^{13}$
First, calculate $1 - 0.0875 = 0.9125$, then raise it to the power of 13 and multiply by 5000. I'll compute this for you. Initial data A0 = 5000 # Initial area in km^2 r = 0.0875 # Annual decrease rate t = 13 # Time in years

Calculate the remaining area after 13 years

A = A0 * (1 - r)**t round(A) # Rounded to the nearest square kilometerThe area of the forest after 13 years will be approximately 1,521 square kilometers.

Do you have any questions or need a detailed explanation?

Here are five related questions to explore this concept further:

1. How would the formula change if the rate of decrease was compounded monthly instead of annually?
2. What would the area be after 20 years at the same rate of decrease?
3. How is exponential decay used in fields like finance or biology?
4. Can we calculate the time it would take for the forest to reduce to half its size?
5. How does the exponential decay formula differ from linear decay?

Tip: When solving exponential problems, remember to convert percentages to decimals and use parentheses to ensure correct calculations!