Headway on four-lane highways: When traffic is flowing on a highway, the headway is the average time between vehicles. On four-lane highways, the probability P that the headway is at least t seconds...

Headway on four-lane highways: When traffic is flowing on a highway, the headway is the average time between vehicles. On four-lane highways, the probability P that the headway is at least t seconds is given to a good degree of accuracy6 by

where q is the average number of vehicles per second traveling one way on the highway. On a four-lane highway carrying an average of 500 vehicles per hour in one direction, what is the probability that the headway is at least 15 seconds? (Note: 500 vehicles per hour is 500 3600 = 0.14 vehicle per second.) b. On a four-lane highway carrying an average of 500 vehicles per hour, what is the decay factor for the probability that headways are at least t seconds? Reminder: An important law of exponents tells us that abc = ab