(a) 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.) (b) C(48) = ___ ,so for a vehicle driving 48 mph on urban streets, the cost of a traffic accident will be _______ 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 and 50 miles per hour. Round your answer to the nearest whole number.)
(a) 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.) (b) C(48) = ___ ,so for a vehicle driving 48 mph on urban streets, the cost of a traffic accident will be _______ 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 and 50 miles per hour. Round your answer to the nearest whole number.)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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(a) 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.)
(b) C(48) = ___ ,so for a vehicle driving 48 mph on urban streets, the cost of a traffic accident will be _______ 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 and 50 miles per hour. Round your answer to the nearest whole number.)
_____
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.
45
Speed s
Cost C
1.3
20
25
30
35
40
50
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
OC = 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
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