Answered

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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 [tex]W \approx -0.414t + 129.549[/tex], where [tex]t[/tex] is the number of minutes and [tex]W[/tex] 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?

A. 150 minutes
B. 160 minutes
C. 170 minutes
D. 180 minutes

Sagot :

GinnyAnswer
To determine after how many minutes the water level would be less than or equal to 64 cups, we will use the equation provided:

[tex]\[ W = -0.414t + 129.549 \][/tex]

where [tex]\( t \)[/tex] is the number of minutes and [tex]\( W \)[/tex] is the level of water in cups.

1. We need to find [tex]\( t \)[/tex] when [tex]\( W \)[/tex] is less than or equal to 64 cups. Let's set up the equation:

[tex]\[ 64 = -0.414t + 129.549 \][/tex]

2. Next, we solve for [tex]\( t \)[/tex]:

[tex]\[ 64 = -0.414t + 129.549 \][/tex]

[tex]\[ 64 - 129.549 = -0.414t \][/tex]

[tex]\[ -65.549 = -0.414t \][/tex]

3. To isolate [tex]\( t \)[/tex], divide both sides of the equation by -0.414:

[tex]\[ t = \frac{-65.549}{-0.414} \][/tex]

4. Simplifying the right-hand side gives us:

[tex]\[ t \approx 158.330917874396 \][/tex]

Therefore, according to the equation, after approximately 158.33 minutes, the water level would be less than or equal to 64 cups.

From the provided options, the closest answer is:

160 minutes.
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