Question

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?

150 minutes
160 minutes
170 minutes
180 minutes

Explanation:

Step1: Set up the inequality

We want to find when $W\leq64$. Substitute $W$ in the equation $W = - 0.414t+129.549$ into the inequality: $-0.414t + 129.549\leq64$.

Step2: Isolate the variable term

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

Step3: Solve for t

Divide both sides by - 0.414. Remember that when dividing an inequality by a negative number, the direction of the inequality sign changes. So, $t\geq\frac{-65.549}{-0.414}\approx158.33$.

Answer:

160 minutes