A commuter flight between two cities in Oregon takes about 40 minutes. The plane will increase its altitude for the first half of the flight until it gets to 18,000 feet, and then it

will descend for the second half of the flight. The plane ascends and descends at a constant rate of 900

feet per minute.

Independent Quantity:

Dependent Quantity:

The data that we have is:

Total time  = 40min

Rate at which ascends or descends = 900ft/min

Maximum height = 18,000 ft.

We can assume that at t = 0 minutes, the plane is on the ground.

Now we can write the height of the plane as a piecewise function of time.

This means that the dependent quantity is the height, and the independent quantity is the time,

The first piece is.

h(t) = (900ft/min)*t   for 0min ≤ t ≤ 20min

We know that the total flight lasts 40 min, so 20 mins represent half of the flight, and we also know that at half the flight the plane reaches the maximum height of 18,000 ft, that checks our equation:

h(20min) = 900ft/min*20min = 18,000ft

And after that points, the plane starts descending at a rate of 900ft/min (now the initial position is 18,000ft), then we can write:

h(t) = 18,000ft - 900ft/min*(t - 20 min) for 20min ≤ t ≤ 40min

Then the function is:

h(t) =  (900ft/min)*t   for 0min ≤ t ≤ 20min

h(t) = 18,000ft - 900ft/min*(t - 20 min) for 20min ≤ t ≤ 40min

Notice that t = 20mins is a value allowed in the two pieces, and gives the same value of h(t) in the two pieces.