The presence of phosphates in certain waste products dumped into a lake promotes the growth of algae. Rampant growth of algae affects the oxygen supply in the water, so an environmental group wishes to estimate the area of algae growth. Group members measure across the algae growth (see the Figure) and obtain the following data (in feet).
Use Simpson's Rule to approximate the area of the algae growth and round your answer to the nearest square foot.
A) 1,110 sq ft
B) 1,553 sq ft
C) 2,641 sq ft
D) 2,019 sq ft
E) 3,573 sq ft

Question

The presence of phosphates in certain waste products dumped into a lake promotes the growth of algae. Rampant growth of algae affects the oxygen supply in the water, so an environmental group wishes to estimate the area of algae growth. Group members measure across the algae growth (see the Figure) and obtain the following data (in feet). 
Use Simpson's Rule to approximate the area of the algae growth and round your answer to the nearest square foot.  ​
A) 1,110 sq ft 
B) 1,553 sq ft 
C) 2,641 sq ft 
D) 2,019 sq ft 
E) 3,573 sq ft

Quizplus · Accepted Answer

We can use Simpson's rule to approximate the area of the algae growth by dividing the curve into small equal segments, finding the area of each segment, and adding them up.

Using Simpson's rule with the given data, we get:

Area ≈ (5/6) h [y0 + 4y1 + 2y2 + 4y3 + ... + 2yn-2 + 4yn-1 + yn]

where h = the width of each segment = 5 ft (since the data is given in intervals of 5 ft), and n = the total number of intervals = 6.

Plugging in the values, we get:

Area ≈ (5/6) × 5 [15.5 + 4(13.5) + 2(17) + 4(24.5) + 2(25.5) + 4(18)]

Area ≈ 1552.5 sq ft

Rounding to the nearest square foot, we get:

Area ≈ 1553 sq ft

Therefore, the best choice is B.

The Presence of Phosphates in Certain Waste Products Dumped into a Lake