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

Answer:

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

Step-by-step 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,

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

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

$12000=-12m$

$m=\frac{12000}{-12}$

$m=-1000$

Substitute in equation (1),

$24800=8(-1000)+b$

$24800=-8000+b$

$24800+8000=b$

$b=32800$

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