Estimate the value of the quantity.
-A swimming pool has a leak. The leak is getting worse. The following table gives the leakage rate every 6 hours.
$\begin{array}{c|c}
\begin{array}{c}
\text { Time } \
\text { (hr) }
\end{array} & \begin{array}{c}
\text { Leakage } \
\text { (gal/hour) }
\end{array} \
\hline 0 & 0 \
6 & 0.6 \
12 & 1.3 \
18 & 1.9 \
24 & 3.0 \
30 & 4.5 \
36 & 5.9 \
42 & 7.0 \
48 & 8.1
\end{array}$

Give the upper estimate for the number of gallons lost.
A) 193.8 gallons
B) 32.3 gallons
C) 145.2 gallons
D) 253.8 gallons

Question

Estimate the value of the quantity.
-A swimming pool has a leak. The leak is getting worse. The following table gives the leakage rate every 6 hours.
$\begin{array}{c|c}
\begin{array}{c}
\text { Time } \
\text { (hr) }
\end{array} & \begin{array}{c}
\text { Leakage } \
\text { (gal/hour) }
\end{array} \
\hline 0 & 0 \
6 & 0.6 \
12 & 1.3 \
18 & 1.9 \
24 & 3.0 \
30 & 4.5 \
36 & 5.9 \
42 & 7.0 \
48 & 8.1
\end{array}$

Give the upper estimate for the number of gallons lost.
A) 193.8 gallons
B) 32.3 gallons
C) 145.2 gallons
D) 253.8 gallons

Quizplus · Accepted Answer

To estimate the upper bound for the total gallons lost, we calculate the leakage rate at the end of each interval multiplied by the interval length (6 hours). Starting from the first non-zero rate at 6 hours (0.6 gal/hour) until the last rate at 48 hours (8.1 gal/hour):- $0.6 \times 6 = 3.6$- $1.3 \times 6 = 7.8$- $1.9 \times 6 = 11.4$- $3.0 \times 6 = 18.0$- $4.5 \times 6 = 27.0$- $5.9 \times 6 = 35.4$- $7.0 \times 6 = 42.0$- $8.1 \times 6 = 48.6$Adding these together gives an upper estimate of the total gallons lost: $3.6 + 7.8 + 11.4 + 18.0 + 27.0 + 35.4 + 42.0 + 48.6 = 193.8$ gallons.

Estimate the Value of the Quantity Give the Upper Estimate for the Number of Gallons Lost