Question

The altitude of an airplane coming in for a landing is represented by the equation shown below, where y represents the altitude,

in feet, of the airplane and x represents the number of minutes the plane has been descending:
y= -1025x + 30,750
Part A:
Create a table for the values when x = 0, 5, 8, 10, 30.
Include worked-out equations used to identify the values within the table.
Part B:
Identify the altitude after 5 minutes and after 30 minutes. Use 1-2 sentences to explain the altitude at these two times and
describe what is happening to the ajrplane at these time intervals.
Part C:
Which ordered pair(from the table in part A) represents the initial value? What does the initial value represent in this problem?
Part D:
What is the rate of change in this equation? What does the rate of change represent in this problem?

Answer 1

Explanation:

Part A:

To create the table, we substitute each of the given values of x into the equation and solve for y:

x y = -1025x + 30,750

0 30,750

5 25,375

8 21,050

10 18,725

30 -7,500

Part B:

The altitude after 5 minutes can be found by substituting x=5 into the equation:

y = -1025(5) + 30,750 = 25,375

The altitude after 30 minutes can be found by substituting x=30 into the equation:

y = -1025(30) + 30,750 = -7,500

After 5 minutes, the altitude of the airplane is 25,375 feet. After 30 minutes, the altitude of the airplane is -7,500 feet, which means the airplane is on the ground. This is because the altitude is decreasing by 1,025 feet every minute, and after 30 minutes, the altitude has decreased to 0 feet, which is the ground level.

Part C:

The ordered pair (0, 30,750) represents the initial value, where x=0. The initial value represents the altitude of the airplane before it started descending. In this problem, the initial value of 30,750 feet represents the altitude of the airplane when it was at cruising altitude.

Part D:

The rate of change in this equation is -1025. The rate of change represents the speed at which the altitude of the airplane is changing per minute. In this problem, the rate of change of -1025 feet per minute means that the altitude of the airplane is decreasing by 1025 feet every minute it descends.