The table below shows the length of skid marks (in feet) left by an automobile w
ID: 3137395 • Letter: T
Question
The table below shows the length of skid marks (in feet) left by an automobile when making emergency stops.
Speed (mph)
20
30
40
50
60
70
80
Length of Skid Marks
24
49
81
118
186
251
317
a.Let X be the speed in miles per hour. Find a quadratic regression model that expresses the braking distance in terms of x. Round coefficients to 3 significant digits. (Begin counting significant digits at the first non-zero digit.)
b.If the skid marks for an emergency stop are 220 feet long, how fast was the car traveling, according to the model?
Speed (mph)
20
30
40
50
60
70
80
Length of Skid Marks
24
49
81
118
186
251
317
Explanation / Answer
a)
Input the data in TI-83 calculator by pressing STAT key, then switch to CALC menu, use the Quadreg feature to find the quadratic regression model as
d = 0.05142857*x^2-0.18571429*x+6.71428571
Round it as
d = 0.0514*x^2-0.186x+6.71
d = 0.051*x^2-0.186x+6.71 [ Try both as 3 significant digits]
b)
Given d=200
0.051*x^2-0.186x+6.71 =200
Using TRACE feature
x =63.4135
x is about 63 mph
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