Between 12:00 _PM and 1:00 _PM, cars arrive at Citibank’s drive-thru at the rate of 6 cars per hour (0.1 car per minute). The following formula from probability can be used to determine the probability that a car will arrive within t minutes of 12:00 _PM:

F(t) = 1 - e^-0.1t

(a) Determine the probability that a car will arrive within 10 minutes of 12:00 PM (that is, before 12:10 _Pm).

(b) Determine the probability that a car will arrive within 40 minutes of 12:00 PM (before 12:40 _Pm).

(c) What value does F approach as at becomes unbounded in the positive direction?

(d) Graph Fusing a graphing utility.

(e) Using INTERSECT, determine how many minutes are needed for the probability to reach 50%.