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

Using Simpson's Rule, we can approximate the area of the algae growth as follows:

Area ≈ [f(x0) + 4f(x1) + 2f(x2) + 4f(x3) + 2f(x4) + ... + 2f(x14) + 4f(x15) + f(x16)] * (b-a)/6

where a = 0, b = 16 (since we have 17 data points), and f(xi) represents the width of the algae growth at the ith measurement point.

Plugging in the given measurements, we get:

Area ≈ [4 + 22 + 29 + 39 + 45 + 48 + 49 + 48 + 44 + 39 + 30 + 23 + 15 + 10 + 5] * (16-0)/6
≈ 1,552.5

Rounding to the nearest square foot, we get the answer as B) 1,553 sq ft.

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