Question: A hydrologist models the water level in a reservoir as $ W(t) = -2t^2 + 12t + 50 $, where $ t $ is time in months since the start of the drought. What is the maximum water level, and at what time does it occur?

Sun, 03 May 2026 04:37:13 +0000

Understanding Reservoir Water Levels: A Hydrology Model Analysis When managing water resources during droughts, accurate modeling of reservoir levels is essential for sustainable planning. One such model used by hydrologists is the quadratic function: $$
W(t) = -2t^2 + 12t + 50
$$ where $ W(t) $ represents the water level in meters and $ t $ is the time in months since the onset of a drought. This article explores the key features of the model—specifically, identifying the maximum water level and the time at which it occurs.