Question

A commercial airliner takes off from a runway with an elevation of 150 feet above sea level. The airliner's altitude above sea level increases at a linear rate of 3,000 feet each minute, m, after its takeoff time until it reaches its cruising altitude of 39,000 feet. Which of the following functions best models the altitude, a, of the airliner before it reaches its cruising altitude?

1) a = 150 + 3,000m
2) a = 39,000 - 3,000m
3) a = 150 + 39,000m
4) a = 39,000 + 3,000m

Answer 1

Option 1, a = 150 + 3,000m, is the correct function that models the airliner's altitude increase before reaching cruising altitude. It accounts for both the initial elevation and the rate of climb per minute.

Step-by-step explanation:

The correct function that models the altitude, a, of the airliner before it reaches its cruising altitude is given by Option 1, which is a = 150 + 3,000m. This linear function starts with the initial elevation of the runway, which is 150 feet above sea level. The term 3,000m represents the rate at which the airliner's altitude increases, with m being the number of minutes after takeoff. The altitude of the airliner increases by 3,000 feet each minute until it reaches the cruising altitude of 39,000 feet. Options 2, 3, and 4 do not correctly represent the linear increase of the altitude after takeoff.