The following table shows the cost C of traffic accidents, in cents per vehicle-mile, as a function of vehicular speed s, in miles per hour, for commercial vehicles driving at night on urban streets. Speed s 20 1.3 25 30 35 0.4 0.1 0.3 40 0.9 2.2 5.8 45 50 Cost C The rate of vehicular involvement in traffic accidents (per vehicle-mile) can be modeled as a quadratic function of vehicular speed s, and the cost per vehicular involvement is roughly a linear function of s, so we expect that C (the product of these two functions) can be modeled as a cubic function of s. (a) Use regression to find a cubic model for the data. (Keep two decimal places for the regression parameters written in scientific notation.) Oc = 0.005643s - 0.2365s + 0.789s - 2.54 C= 0.000422s - 0.0294s + 0.562s -1.65 C=0.001245s - 0.1234s Oc- 0.000348s - 0.0946s + 0.341s - 1.91 Oc= 0.000526s - 0.0351s + 0.976s - 0.34 OC= + 0.652s - 0.48 answer means in practical terms. (Use the model found in part (a). Round your answer to two decimal places.) mph at night on urban streets, the cost of a traffic accident will be [ (b) Calculate C(48) and explain what your C(48) = [ ). so for a vehicle driving |cents per vehicle mile. (c) At what speed is the cost of traffic accidents (for commercial vehicles driving at night on urban streets) at a minimum? (Use the model found in part (a). Consider speeds between 20 a 50 miles per hour. Round your answer to the nearest whole number.) mph

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The following table shows the cost C of traffic accidents, in cents per vehicle-mile, as a function of vehicular speed s, in miles per hour, for commercial vehicles driving at night on urban streets.
Speed s
20
25
30
35
40
45
50
Cost C
1.3
0.4
0.1
0.3
0.9
2.2
5.8
The rate of vehicular involvement in traffic accidents (per vehicle-mile) can be modeled as a quadratic function of vehicular speed s, and the cost per vehicular involvement is roughly a linear
function of s, so we expect that C (the product of these two functions) can be modeled as a cubic function of s.
(a) Use regression to find a cubic model for the data. (Keep two decimal places for the regression parameters written in scientific notation.)
OC = 0.005643s - 0.2365s + 0.789s - 2.54
C = 0.000422s - 0.0294s + 0.562s - 1.65
OC = 0.001245s - 0.1234s + 0.652s - 0.48
Oc = 0.000348s - 0.0946s - 0.341s - 1.91
Oc = 0.000526s - 0.0351s + 0.976s - 0.34
(b) Calculate C(48) and explain what your answer means in practical terms. (Use the model found in part (a). Round your answer to two decimal places.)
C(48) =|
, so for a vehicle driving
mph at night on urban streets, the cost of a traffic accident will be
cents per vehicle mile.
%3D
(c) At what speed is the cost of traffic accidents (for commercial vehicles driving at night on urban streets) at a minimum? (Use the model found in part (a). Consider speeds between 20 and
50 miles per hour. Round your answer to the nearest whole number.)
mph
Transcribed Image Text:The following table shows the cost C of traffic accidents, in cents per vehicle-mile, as a function of vehicular speed s, in miles per hour, for commercial vehicles driving at night on urban streets. Speed s 20 25 30 35 40 45 50 Cost C 1.3 0.4 0.1 0.3 0.9 2.2 5.8 The rate of vehicular involvement in traffic accidents (per vehicle-mile) can be modeled as a quadratic function of vehicular speed s, and the cost per vehicular involvement is roughly a linear function of s, so we expect that C (the product of these two functions) can be modeled as a cubic function of s. (a) Use regression to find a cubic model for the data. (Keep two decimal places for the regression parameters written in scientific notation.) OC = 0.005643s - 0.2365s + 0.789s - 2.54 C = 0.000422s - 0.0294s + 0.562s - 1.65 OC = 0.001245s - 0.1234s + 0.652s - 0.48 Oc = 0.000348s - 0.0946s - 0.341s - 1.91 Oc = 0.000526s - 0.0351s + 0.976s - 0.34 (b) Calculate C(48) and explain what your answer means in practical terms. (Use the model found in part (a). Round your answer to two decimal places.) C(48) =| , so for a vehicle driving mph at night on urban streets, the cost of a traffic accident will be cents per vehicle mile. %3D (c) At what speed is the cost of traffic accidents (for commercial vehicles driving at night on urban streets) at a minimum? (Use the model found in part (a). Consider speeds between 20 and 50 miles per hour. Round your answer to the nearest whole number.) mph
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