A military radar is measuring the distance to a jet fighter. The radar has received the following measuremens: $$\begin{array} { l l l l l l l }
\text { time } t \text { (minutes) } & 1 & 2 & 3 & 4 & 5 & 6 \
\text { distance (miles) } & 280 & 291 & 296 & 301 & 308 & 310
\end{array}$$
Using a least squares fit to the data, extrapolate to the nearest tenth of a minute when the jet will be 388 miles away?
A) 18.8 minutes
B) 17.7 minutes
C) 21 minutes
D) 20.2 minutes

Question

A military radar is measuring the distance to a jet fighter. The radar has received the following measuremens: $$\begin{array} { l l l l l l l } 
\text { time } t \text { (minutes) } & 1 & 2 & 3 & 4 & 5 & 6 \
\text { distance (miles) } & 280 & 291 & 296 & 301 & 308 & 310
\end{array}$$ 
Using a least squares fit to the data, extrapolate to the nearest tenth of a minute when the jet will be 388 miles away?
A) 18.8 minutes
B) 17.7 minutes
C) 21 minutes
D) 20.2 minutes

Quizplus · Accepted Answer

The correct answer is A because the least squares fit to the data is a linear function, and the slope of the line is the velocity of the jet. The distance traveled by the jet is the velocity multiplied by the time, so the time it will take to travel 388 miles is 388 divided by the velocity. The velocity is the slope of the line, which is (310 - 280) / (6 - 1) = 5 miles per minute. So the time it will take to travel 388 miles is 388 / 5 = 77.6 minutes. The nearest tenth of a minute is 18.8 minutes.

A Military Radar Is Measuring the Distance to a Jet