Question

Emely, an air traffic controller is monitoring the altitudes of four planes. The four equations below show y, the distance in feet of each plane above the ground, after t minutes of descent.

Plane A: -400t + 12,000

Plane B: -800t + 28,000

Plane C: -200t + 13,500

Plane D: -500t + 30,000


a. Which plane is descending at the slowest rate?
b. Which plane began its descent from the highest altitude?

Answer 1

Plane C is descending at the slowest rate, descending at a rate of 200 feet/minute. Plane D started its descent from the highest altitude, beginning at 30,000 feet.

Step-by-step explanation:

To answer question (a), which plane is descending at the slowest rate, we look at the coefficients of t in the equations. These coefficients represent the rates of descent.

• Plane A: -400t + 12,000
• Plane B: -800t + 28,000
• Plane C: -200t + 13,500
• Plane D: -500t + 30,000

Comparing the rates of descent (ignoring the negative sign, which indicates a descent), we have:
Plane A: 400 feet/minute
Plane B: 800 feet/minute
Plane C: 200 feet/minute
Plane D: 500 feet/minute

Therefore, Plane C is descending at the slowest rate.

To answer question (b) regarding which plane began its descent from the highest altitude, we look at the constant term in each equation, which represents the initial altitude.

• Plane A: 12,000 feet
• Plane B: 28,000 feet
• Plane C: 13,500 feet
• Plane D: 30,000 feet

Plane D started from 30,000 feet, which is the highest altitude among the four planes.