6: An entomologist models the growth of a pollinator population. Starting with 120 bees, the population increases by 15% each week due to reproductive success. After 4 weeks, how many bees are estimated to be in the population? (Round to the nearest whole number.)

["Modeling Pollinator Growth: How Bees Multiply Over Time", "Understanding how pollinator populations grow is essential for ecological conservation and agricultural sustainability. In this article, we explore a real-world example of population modeling using exponential growth, focusing on a bee colony’s development. Starting with 120 bees, this colony thrives due to a weekly growth rate of 15%—a model often used in entomology to predict population dynamics.", "### The Mathematical Model of Bee Population Growth", "Exponential growth describes a population that increases by a fixed percentage each time period. The general formula is:", "[\nP(t) = P_0 \ imes (1 + r)^t\n]", "Where:\n- (P(t)) = population at week (t)\n- (P_0) = initial population (120 bees)\n- (r) = weekly growth rate (15% = 0.15)\n- (t) = number of weeks (4 weeks in this case)", "### Applying the Formula Step-by-Step", "Start with:\n- Initial population (P_0 = 120)\n- Growth rate (r = 0.15)\n- Number of weeks (t = 4)", "Calculate the population after each week:", "[\nP(1) = 120 \ imes (1.15)^1 = 120 \ imes 1.15 = 138\n]\n[\nP(2) = 138 \ imes 1.15 = 158.7\n]\n[\nP(3) = 158.7 \ imes 1.15 \approx 182.51\n]\n[\nP(4) = 182.51 \ imes 1.15 \approx 209.89\n]", "### Final Estimate", "After rounding to the nearest whole number, the estimated bee population after 4 weeks is 210 bees.", "This projection supports entomologists’ efforts to manage pollinator health, forecast colony resilience, and protect vital ecosystems dependent on bee pollination.", "### Why This Matters", "Accurate population modeling helps predict resource needs, inform conservation strategies, and highlight the importance of habitat preservation. The 15% weekly increase observed here reflects both natural reproductive cycles and favorable environmental conditions—key drivers in sustaining pollinator species amid global ecological challenges.", "---", "Round to the nearest whole number: 209.89 → 210\nModeled using entomological principles of exponential growth in bee populations."]