titus works at a hotel. part of his job is to keep the complimentary pitcher of water at least half full and…

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 $wapprox - 0.414t + 129.549$, where $t$ is the number of minutes and $w$ 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?\n150 minutes\n160 minutes\n170 minutes\n180 minutes

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 $wapprox - 0.414t + 129.549$, where $t$ is the number of minutes and $w$ 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?\n150 minutes\n160 minutes\n170 minutes\n180 minutes

Answer

Answer:

C. 170 minutes

Explanation:

Step1: Set up the inequality

Set $W\leq64$, so $- 0.414t + 129.549\leq64$.

Step2: Isolate the variable term

Subtract 129.549 from both sides: $-0.414t\leq64 - 129.549$. $-0.414t\leq - 65.549$.

Step3: Solve for t

Divide both sides by - 0.414. Remember to reverse the inequality sign when dividing by a negative number. $t\geq\frac{-65.549}{-0.414}\approx158.33$. Since we are looking for the time when the water level is less than or equal to 64 cups, and among the given options, 170 minutes is the closest value that satisfies the inequality.