Final answer:
The correct equation representing the airplane's height above ground as a function of time in minutes is H(t) = 30000 - 2000t. It would take the airplane 6 minutes to reach 18,000 feet based on the given rate of descent, but this answer is not in the provided options.
Step-by-step explanation:
The student has asked for two things: first, to identify the correct equation to represent the airplane's height above the ground as a function of time in minutes; and second, to calculate the time it will take for the airplane to reach a height of 18,000 feet above the ground. To begin, considering the airplane is descending at a rate of 2000 feet per minute, the correct equation to represent this would be H(t) = 30000 - 2000t, where H represents the height in feet and t represents the time in minutes (Option a).
To find out how many minutes it will take for the plane to reach a height of 18,000 feet, we can set the equation H(t) = 30000 - 2000t equal to 18,000 and solve for t. This gives us:
18000 = 30000 - 2000t
2000t = 30000 - 18000
2000t = 12000
t = 12000 / 2000
t = 6
Thus, it will take the airplane 6 minutes to reach a height of 18,000 feet, which is not one of the options given. Therefore, there may be an error within the provided options or the question itself.