The population after 15 days is \( 500 \times 2^5 = 500 \times 32 = 16000 \).

["Understanding Population Growth: The Case of 15 Days Population Doubling", "When exploring exponential population growth, a common mathematical expression helps illustrate how rapidly populations can expand under ideal conditions. Consider a scenario where a population doubles every 3 days, and we calculate the population after 15 days. The formula often used is:", "[\nP = 500 \ imes 2^5\n]\n[\nP = 500 \ imes 32 = 16,000\n]", "This simple calculation reveals that starting from an initial population of 500 individuals, doubling every 15 days (which corresponds to 5 doubling periods in 15 days) results in a population of 16,000.", "Why Doubling Dynamics Matter in Population Models\nPopulation growth modeled by exponential functions like ( P = P_0 \ imes 2^{t/n} ) is widely used in ecology, demography, and epidemiology to describe how species or human communities can expand rapidly when resources are abundant and constraints are minimal. In this example, doubling every 15 days reflects intense growth — a critical benchmark for understanding carrying capacity, resource demand, and long-term sustainability.", "How 15 Days Becomes a Key Timeframe\nChoosing 15 days as the growth interval offers a clear, manageable timeframe for modeling. For human populations, 3–5 days is often cited as a rough estimate for doubling under strong migration and high birth rates, while doubling every 15 days indicates an extreme but instructive example of exponential acceleration. This kurz timeframe helps policymakers, researchers, and educators visualize tipping points and the profound impact of sustained growth.", "Environmental and Social Implications\nWhile modeling exponential growth is informative, real-world constraints such as food availability, space, health infrastructure, and environmental degradation eventually limit unbounded expansion. The doubling formula underscores why early intervention is vital in population planning — a rapid rise from 500 to 16,000 in just 15 days could strain infrastructure and resources beyond sustainable levels.", "Conclusion\nThe population after 15 days, calculated as ( 500 \ imes 2^5 = 16,000 ), exemplifies the dramatic effects of exponential growth. It serves as a powerful reminder of how quickly populations can expand when growth conditions remain favorable — highlighting both the potential and the challenges of demographic change. Understanding these dynamics helps inform smarter decisions for sustainable development and resource management.", "---", "Keywords: exponential population growth, doubling time, population doubling formula, 15-day growth model, ( P = 500 \ imes 2^5 = 16000 ), ecology modeling, demography, sustainable development."]