Question

An airplane 30,000 feet above the ground begins descending at a rate of 2,000 feet per minute. Write an equation to model the situation. Find the altitude(height above the ground) of the plane after 5 minutes.

Answer 1

Let's define

x: time, in minutes

y: altitude, in feet

This situation can be modeled with a line

Equation of a line:

y = mx + b

where m is the slope and b is the y-intercept

At the beginning, time, that is, x = 0, and the altitude (y) = 30000 ft. Then, b = 30000 in the equation.

The slope relates the change in variable y with respect to the change in variable x. In the context of this problem, the descending rate of 2000 ft per minute is the slope. Then, m = -2000, notice that the airplane is descending, so the sope is negative.

The equation is:

y = -2000x + 30000

The altitude after 5 minutes is found replacing x = 5 into the equation, as follows:

y = -2000(5) + 30000

y = -10000 + 30000

y = 20000

The altitude after 5 minutes is 20000 ft