Question

After descending for 8 minutes, an airplane is at an altitude of 24800 feet. After 20 minutes, the plane's altitude is 12800 feet. Assuming a linear function, write an equation in the form a(t)=mt+b that shows the altitude, a, after t minutes of descent.

Answer 1

The equation form is,
`a(t)=-1000t+32800`

Explanation:

Given : After descending for 8 minutes, an airplane is at an altitude of 24800 feet. After 20 minutes, the plane's altitude is 12800 feet.

To find : Write an equation in the form a(t)=mt+b that shows the altitude, a, after t minutes of descent ?

Solution :

The equation is in form,
`a(t)=mt+b`

Where, 't' is the time in minutes and 'a' is the altitude,

After descending for 8 minutes, an airplane is at an altitude of 24800 feet.

i.e. a=24800 and t=8

Substitute in the equation,

`24800=m(8)+b`

`24800=8m+b` ......(1)

After 20 minutes, the plane's altitude is 12800 feet.

i.e. a=12800 and t=20

Substitute in the equation,

`12800=m(20)+b`

`12800=20m+b` ......(2)

Solving (1) and (2) by subtracting them,

`24800-12800=8m+b-(20m+b)`

`12000=8m+b-20m-b`

`12000=-12m`

`m=(12000)/(-12)`

`m=-1000`

Substitute in equation (1),

`24800=8(-1000)+b`

`24800=-8000+b`

`24800+8000=b`

`b=32800`

So, The equation form is,
`a(t)=-1000t+32800`