Titus works at a hotel. Part of his job is to keep the complimentary pitcher of water at least half full and always with ice. When he starts his shift, the water level shows 8 gallons, or 128 cups of water. As the shift progresses, he records the level of the water every 10 minutes. After 2 hours, he uses a regression calculator to compute an equation for the decrease in water. His equation is W approximately equal to negative 0 point 4 1 4 t plus 129 point 5 4 9 , where t is the number of minutes and cap w is the level of water. According to the equation, after about how many minutes would the water level be less than or equal to 64 cups?
Set the equation’s water level equal to 64 cups to find when it reaches the half-full threshold: 64 = −0.414t + 129.549. Solving gives t ≈ 158.3 minutes; because the water level is decreasing, it will be at or below 64 cups after about 160 minutes. The correct choice is D, 160 minutes.
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