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? Choose 1 answer: (A) a(m)=150+(39,000)/(3,000)m (B) a(m)=39,150-3,000 m (C) a(m)=150+3,000 m (D) a(m)=3,000+150 m

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Understand the problem: Understand the problem. We need to find a function that models the altitude of the airliner as it climbs from the runway to its cruising altitude. The initial altitude is 150 feet, and the rate of climb is 3,000 feet per minute until it reaches 39,000 feet.Analyze the answer choices: Analyze the answer choices. We are given four function options to choose from. We need to select the one that correctly represents the altitude as a function of time in minutes.Evaluate option A: Evaluate option A. Option A suggests that the altitude is a function of time where the altitude increases by the ratio of the cruising altitude to the rate of climb per minute. This does not make sense because the rate of climb is not a ratio but a fixed amount per minute.Evaluate option B: Evaluate option B. Option B suggests that the altitude starts at 39,150 feet and decreases by 3,000 feet per minute. This is incorrect because the airliner starts at 150 feet and increases in altitude, not decreases.Evaluate option C: Evaluate option C. Option C suggests that the altitude is 150 feet plus 3,000 feet times the number of minutes. This correctly represents a starting altitude of 150 feet and an increase of 3,000 feet per minute.Evaluate option D: Evaluate option D. Option D suggests that the altitude is a constant 3,150 feet, which does not account for the increase in altitude over time.Choose the correct function: Choose the correct function. Based on the analysis, option C is the correct function because it starts at the correct initial altitude and increases at the correct rate per minute.

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