Original question written by FE Exam AI Prep from the public FE Civil exam specification. Before release, a solver model re-derived the answer twice from the question alone, without its answer key, and a critic model checked the result, and the arithmetic was re-run as an executable calculation. No licensed engineer reviews these questions. It is not an NCEES question and does not come from any NCEES practice exam. FE Exam AI Prep is an independent study tool and is not affiliated with, endorsed by, or sponsored by NCEES.
EASYlinear interpolation
Linear Interpolation: FE Civil practice problem 3
For the Red River detention pond retrofit, a materials reviewer preparing a constructability analysis linearly interpolates between (16, 72) and (24, 132). What value corresponds to x = 19.2?
- A96.00
- B65.29
- C71.63
- D84.80
Show the answer and worked solution
Answer: A — 96.00
Worked solution
- Step 1. Use linear interpolation
y = y1 + (x - x1)(y2 - y1)/(x2 - x1)
- Step 2. Substitute values
y = 72 + (19.2 - 16)(132 - 72)/(24 - 16) = 96
Why the other choices are wrong
- Choice B
- This value equals the correctly interpolated result of 96.00 multiplied by about 1.18 rather than being computed from y1 + (x - x1) * (y2 - y1) / (x2 - x1) between the points x = 16 and x = 24, so it exceeds the true interpolated value at x = 19.2.
- Choice C
- This number equals the true interpolated value of 96.00 multiplied by roughly 0.78 instead of evaluating y1 + (x - x1) * (y2 - y1) / (x2 - x1) across the stated pair of points, so it understates the straight-line result at x = 19.2.
- Choice D
- This answer equals the correct interpolated value of 96.00 multiplied by close to 1.45, a scale-up that does not come from any single term in y1 + (x - x1) * (y2 - y1) / (x2 - x1), so it substantially overstates the true interpolated result at x = 19.2.