Question

A plane is currently flying at 20,000 feet and begins to descend at a rate of 800 feet per minute. a. Write a function for the height of the plane in terms of how long it has been since it began to descend. b. How long will it take for the plane to reach 1500 feet? c. How long will it take for the plane to touch down?

Answer 1

Okay, here we have this:

Considering the provided information, we are going to write the requested function and find the requested values, so we obtain the following:

a)

Then it will correspond to a linear function where we will take as the change in slope and the initial height will be the y-intercept, since it is instant zero, then we have:

f(x)=-800x+20000

b)

Now let's equal 1500 to know how long it will take to reach that height

f(x)=-800x+20000

1500=-800x+20000

800x=18500

x=18500/800

x=185/8

x=23.125

Finally we obtain that it will take 23.125 minutes for the plane to reach 1500 feet.

c)

Now let's equal 0 to know how long it will take for the plane to touch down:

f(x)=-800x+20000

0=-800x+20000

800x=20000

x=20000/800

x=200/8

x=25

Finally we obtain that that it will take 25 minutes for the plane to touch down