A helicopter, initially hovering 40 feet above the ground, begins to gain altitude at a rate of 21 feet per second. Which of the following functions represents the helicopter’s altitude above the ground y, in feet, t seconds after the helicopter begins to gain altitude?

Options

A. y = 40 + 21
B. y = 40 + 21t
C. y = 40 − 21t
D. y = 40t + 21

Answer

B

Explanation

It’s given that the helicopter’s initial height is 40 feet above the ground and that when the helicopter’s altitude begins to increase, it increases at a rate of 21 feet per second. Therefore, the altitude gain t seconds after the helicopter begins rising is represented by the expression 21t. Adding this expression to the helicopter’s initial height gives the helicopter’s altitude above the ground y, in feet, t seconds after the helicopter begins to gain altitude: y = 40 + 21t.
Choice A is incorrect. This is the helicopter’s altitude above the ground 1 second after it began to gain altitude, not t seconds after it began to gain altitude. Choice C is incorrect because adding the expression −21t makes this function represent a decrease in altitude. Choice D is incorrect and is the result of using the initial height of 40 feet as the rate at which the helicopter’s altitude increases per second and the rate of 21 feet per second as the initial height.