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
To find the answer, we need to find the equation of the linear function that represents the height of the airplane above the ground level.
We know that after 2 minutes, the height is 3915 meters, and after 9 minutes, the height is 2025 meters.
Let's represent the height, h, as a function of time, t, in minutes:
h = mt + b
To find the equation, we need to find the values of m and b.
Using the given information, we have two equations:
3915 = 2m + b (equation 1)
2025 = 9m + b (equation 2)
We can solve these two equations simultaneously to find the values of m and b.
Subtracting equation 1 from equation 2:
-1890 = 7m
Dividing both sides by 7:
m = -270
Now substitute the value of m into equation 1 to solve for b:
3915 = 2(-270) + b
3915 = -540 + b
b = 3915 + 540
b = 4455
So the equation of the linear function is:
h = -270t + 4455
Now we need to find the value of t when the height, h, is 0. This represents the time when the plane lands at the airport.
0 = -270t + 4455
Solving for t:
270t = 4455
t = 4455 / 270
t = 16.5 minutes
So it will take the plane 16.5 minutes to land at the airport after it started to descend.
The correct answer is:
16.5 minutes
(Note: The options provided are rounded to the nearest whole number, so we can choose the closest option, which is 16 minutes.)