Solve the problem.
-The following table shows the rate of water flow (in gal/min) from a stream into a pond during a 30 -minute period after a thunderstorm. Use Simpson's Rule to estimate the total amount of water flowing into the pond during this period. Round your answer to the nearest gallon.
$\begin{array}{l|l}
\text { Time (min) } & \text { Rate (gal/min) } \
\hline 0 & 200 \
5 & 250 \
10 & 300 \
15 & 250 \
20 & 220 \
25 & 200 \
30 & 150
\end{array}$

A) 7975 gal
B) 6383 gal
C) 6983 gal
D) 6975 gal

Question

Solve the problem.
-The following table shows the rate of water flow (in gal/min) from a stream into a pond during a 30 -minute period after a thunderstorm. Use Simpson's Rule to estimate the total amount of water flowing into the pond during this period. Round your answer to the nearest gallon.
$\begin{array}{l|l}
\text { Time (min) } & \text { Rate (gal/min) } \
\hline 0 & 200 \
5 & 250 \
10 & 300 \
15 & 250 \
20 & 220 \
25 & 200 \
30 & 150
\end{array}$

A) 7975 gal
B) 6383 gal
C) 6983 gal
D) 6975 gal

Quizplus · Accepted Answer

Using Simpson's Rule, we first need to find the interval between the given data points:
$$h = \frac{b-a}{6} = \frac{30-0}{6} = 5$$

Then, we can use Simpson's Rule formula:
$$\int_{a}^{b} f(x) dx \approx \frac{h}{3} [f(x_0) + 4f(x_1) + 2f(x_2) + 4f(x_3) + 2f(x_4) + 4f(x_5) + f(x_6)]$$

Substituting the given values, we get:
$$\begin{aligned} &\int_{0}^{30} f(x) dx \approx \frac{5}{3} [200 + 4(250) + 2(300) + 4(250) + 2(220) + 4(200) + 150] \ &\approx 6983.33 \approx 6983 	ext{ (rounded to the nearest gallon)} \end{aligned}$$

Therefore, the best choice is C, which is the closest rounded value to the calculated estimate.

Solve the Problem A) 7975 Gal B) 6383 Gal C) 6983 Gal D)

Solve the Problem A) 7975 Gal
B) 6383 Gal
C) 6983 Gal
D)