Traffic accidents: The following table shows the costC 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...

Traffic accidents: The following table shows the costC 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.

The rate of vehicular involvement in traffic accidents (per vehicle-mile) can be modeled66 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 coefficients 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.)