Answered: The per capita consumption of…

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

6th Edition

ISBN:9781337111348

Author:Bruce Crauder, Benny Evans, Alan Noell

Publisher:Bruce Crauder, Benny Evans, Alan Noell

Chapter5: A Survey Of Other Common Functions

Section5.6: Higher-degree Polynomials And Rational Functions

Problem 3E: Traffic Accidents The following table shows the cost C of traffic accidents. in cents per...

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Traffic Accidents 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. b. Calculate C(42) and explain what your answer means in practical terms. c. At what speed is the cost of traffic accidents for commercial vehicles driving at night on urban streets at a minimum? Consider speeds between 20 and 50 miles per hour.
Postal Rates U.S postal rates have steadily increased since 1932. Using data depicted in the table for the years 1932-2013, the cost in cents to mail a single letter can be modelled using a quadratic formula as follows: C(t)=0.007756t20.04258t+0.7585 where t is the number of years since 1932. Source: U.S. Postal Service. Year Cost Year Cost 1932 3 1988 25 1958 4 1991 29 1963 6 1995 32 1971 8 2001 34 1974 10 2002 37 1975 13 2006 39 1978 15 2007 41 1981 18 2008 42 1981 20 2009 44 1985 22 2012 45 2013 46 a. Find the predicted cost of mailing a letter in 1982 and 2002 and compare these estimates with the actual rates. b. Find the rate of change of the postage cost for the years 1982 and 2002 and interpret your results. c. Using the regression feature on a graphing calculator, find a cubic function that models these data, letting t=0 correspond to the year 1932. Then use your answer to find the rate of change of the postage cost for the years 1982 and 2002. d. Discuss whether the quadratic or cubic function best describes the data. Do the answers from part b or from part c best describe the rate that postages was going up in the years 1982 and 2002? e. Explore other functions that could be used to model the data, using the various regression features on a graphing calculator, and discuss to what extent any of them are useful descriptions of the data. f. g.

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