The time t (in minutes) for a small plane to climb to an altitude of h feet is modeled by t = 50 log [18,000/(18,000 − h)] where 18,000 feet is the plane's absolute ceiling.
(a) Determine the domain of the function in the context of the problem.
(b) Use a graphing utility to graph the function and identify any asymptotes.
(c) As the plane approaches its absolute ceiling, what can be said about the time required to increase its altitude?
(d) Find the time it takes for the plane to climb to an altitude of 4000 feet.