A population of deer is increasing at a rate of \( 12 \% \) per year. If this rate of growth remains the same and the population starts out with 250 deer, approximately how many deer will there be after 5 years? a.) 441 deer b.) 387 deer c.) 265 deer d.) 508 deer

To find the population of deer after 5 years given a 12% annual growth rate, we can use the formula for compound interest, which can also be applied to populations: \[ P = P_0 (1 + r)^t \] where \( P_0 \) is the initial population (250 deer), \( r \) is the growth rate (0.12), and \( t \) is the time in years (5). Plugging in the numbers: \[ P = 250 (1 + 0.12)^5 \approx 250 (1.7623) \approx 440.58 \] Rounding gives us approximately 441 deer. So the answer is **a.) 441 deer**. While mathematicians and scientists have studied exponential growth for centuries, it's fascinating to realize these principles underpin so much of our environment, from animal populations to interest on savings accounts. This concept isn't just a dry formula—it's a reflection of how living things adapt and survive, often leading to surprising growth patterns in nature! In the real world, understanding population dynamics can help in wildlife management, conservation efforts, and urban planning. For example, if deer populations increase too rapidly, they may outstrip their food sources, leading to starvation or disease. On the flip side, wildlife managers can use these equations to predict needed interventions to maintain a balance in ecosystems.