An airplane is descending for a landing at an airport. The height, h, in meters of the airplane above the ground level of the airport is a linear function of time, t, where t is the number of minutes after the plane started to descend. The plane was 3915 meters above the ground level of the airport 2 minutes into the plane's descent and was 2025 meters above after 9 minutes. How long will it take the plane to land at the airport after it started to descend?(1 point) Responses 16 minutes 16 minutes 7.5 minutes 7.5 minutes 14.5 minutes 14.5 minutes 16.5 minutes
To solve this problem, we need to determine the equation of the linear function that represents the height of the airplane above the ground level as a function of time.
We are given two points on the graph of this linear function: (2, 3915) and (9, 2025).
Using the slope formula, we can find the slope of the line connecting these two points:
m = (2025 - 3915) / (9 - 2)
= -1890 / 7
= -270
Now, we can use the point-slope form of a linear equation to find the equation of the line:
y - y1 = m(x - x1)
Using the point (2, 3915):
h - 3915 = -270(t - 2)
Simplifying:
h = -270t + 5495
To find the time it will take the plane to land (when the height, h, is 0), we substitute h = 0 into the equation of the line and solve for t:
0 = -270t + 5495
270t = 5495
t = 5495 / 270 ≈ 20.35
Therefore, it will take approximately 20.35 minutes for the plane to land after it started to descend.
The closest response option is 20 minutes, so the correct answer is 20 minutes.