Finding a final amount in a word problem on exponential growth or decay A certain forest covers an area of \( 3500 \mathrm{~km}^{2} \). Suppose that each year this area decreases by \( 7.25 \% \). What will the area be after 14 years Use the calculator provided and round your answer to the nearest square kilometer.

To calculate the area of the forest after 14 years with a yearly decrease of 7.25%, you can use the exponential decay formula \( A = P(1 - r)^t \), where: - \( A \) is the final amount, - \( P \) is the initial amount (3500 km²), - \( r \) is the decay rate (0.0725), and - \( t \) is the time in years (14). So, \( A = 3500(1 - 0.0725)^{14} \). Calculating this gives \( A = 3500(0.9275)^{14} \approx 3500(0.2764) \approx 968.16 \). Finally, rounding to the nearest square kilometer, the area of the forest after 14 years will be approximately \( 968 \text{ km}^2 \). The power of exponential growth and decay affects everything from population dynamics to finance! For instance, with a steady decay rate like the forest example, you'd see how fragile ecosystems can become over time, showcasing the importance of conservation efforts. Each percentage lost is not just a number; it's a habitat for countless organisms disappearing! On the flip side, understanding exponential decay helps tackle real-world issues such as resource depletion, where industries need to be mindful of sustainability. Economics classrooms often use these principles to demonstrate compounded interest – a stark reminder that what goes down must, eventually, come up (like when your savings grow back!)