Q14 · 2023 · Technology-activeSimple familiar4 marks
QUESTION 14 (4 marks)
At a certain location, a biologist measures the width of a river to be 12 m. She also records the depth of the river at regular 2 m interval widths as shown.
| Width (m) | 0 | 2 | 4 | 6 | 8 | 10 | 12 |
|---|---|---|---|---|---|---|---|
| Depth (m) | 0.52 | 2.15 | 3.70 | 4.27 | 3.32 | 1.28 | 0.59 |
The biologist estimates the cross-sectional area of the river at this location to be 15 m.
Use Simpson’s rule to evaluate the reasonableness of this estimation. Justify your area calculation and decision regarding reasonableness using mathematical reasoning.
WORKED SOLUTION
4 marksQCAA guide · typeset solution
ANSWER
Simpson’s rule gives approximately m; the 15 m estimate is not reasonable.
Worked solution
The interval width is . Simpson’s rule gives
Since 15 m is less than half this estimate, the biologist’s estimate is not reasonable.
determines the interval width
substitutes the data into Simpson’s rule
determines the cross-sectional area
evaluates the reasonableness of the stated estimate using mathematical reasoning
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