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.
