The consumption of water by a Water Company satisfies the empirical equation; V= 1.50𝘵 + 0.008𝘵² . Where V is the volume of water in cubic feet and t is the time in months. What is the consumption in 120 𝘥𝘢𝘺𝘴 in units of 𝘭𝘪𝘵𝘳𝘦𝘴? [Assume 1.0 f t³ ∼ 28.32 𝘭𝘪𝘵𝘳𝘦].
Question
The consumption of water by a Water Company satisfies the empirical equation; V= 1.50𝘵 + 0.008𝘵² . Where V is the volume of water in cubic feet and t is the time in months. What is the consumption in 120 𝘥𝘢𝘺𝘴 in units of 𝘭𝘪𝘵𝘳𝘦𝘴? [Assume 1.0 f t³ ∼ 28.32 𝘭𝘪𝘵𝘳𝘦].
Solution
First, we need to convert the time from days to months since the given equation uses time in months. There are approximately 30.44 days in a month. So, 120 days is about 3.94 months.
Next, we substitute t = 3.94 into the equation V = 1.50t + 0.008t² to find the volume of water consumed in cubic feet.
V = 1.50(3.94) + 0.008(3.94)² V = 5.91 + 0.123 V = 6.033 cubic feet
Finally, we convert the volume from cubic feet to litres using the given conversion factor 1.0 ft³ = 28.32 litres.
Volume in litres = 6.033 ft³ * 28.32 litres/ft³ Volume in litres = 170.77 litres
So, the water consumption in 120 days is approximately 170.77 litres.
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