Chapter 5.6, Problem 3E

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 $C\left(42\right)$ 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.)