A hydrologist studies a reservoir that loses water due to evaporation at a rate of 3% of its volume per week. If the initial volume is 1,000,000 cubic meters, what is the volume after two weeks?

Wed, 06 May 2026 03:52:45 +0000

**Why reservoir evaporation matters—and how math reveals the long-term impact** In an era of growing concerns over water security, understanding how much water remains in a reservoir over time is more relevant than ever. A hydrologist studies a reservoir that loses 3% of its volume each week due to evaporation—a natural process accelerating in many U.S. regions amid rising temperatures and prolonged droughts. As Americans seek clearer insights into water supply sustainability, this simple calculation reveals not just what *is* lost, but the gradual decline hidden beneath the surface. With an initial volume of 1,000,000 cubic meters, this reservoir begins a slow but steady transformation, offering a lens into broader environmental patterns. The math behind this change reflects real-world challenges that affect agriculture, cities, and ecosystems alike. Why are hydrologists tracking evaporation at 3% per week? The question reflects increasing awareness of water loss in key storage systems. Evaporation accounts for significant volume reduction in reservoirs worldwide, particularly in arid or hot climates across the American West and Southwest. Understanding this loss helps planners forecast shortages, adjust allocations, and develop smarter conservation strategies. For curious learners exploring water management trends, this conversion—that 3% weekly loss compounds over time—unsettles intuitive expectations, showing how small weekly deductions accumulate into measurable shortages after just two weeks. Let’s break down how a reservoir volume shrinks when 3% of its total mass evaporates each week. Using basic exponential decay, each week sees 97% of the water remain. After the first week, 1,000,000 cubic meters reduces to 970,000 cubic meters. In the second week, another 3% evaporates from 970,000, leaving 940,900 cubic meters. While not dramatic in two short weeks, this pattern highlights why steady evaporation losses matter—especially when repeated across seasons. For decision-makers and residents alike, this understanding deepens the urgency of protecting water resources with data-driven care.