Question

After 3 minutes, a submarine had descended to −320 feet. After 8 minutes, the submarine had descended to −420 feet. Assuming a linear function, write an equation in the form d(t)=mt+b that shows the depth, d(t), after t minutes

Answer 1

`d(t) = -20t - 260`

Explanation:

The depth function is:

`d(t) = mt + b`

After 3 minutes, a submarine had descended to −320 feet.

This means that
`d(3) = -320`. So

`d(t) = mt + b`

`-320 = 3m + b`

After 8 minutes, the submarine had descended to −420 feet.

This means that
`d(8) = -420`. So

`d(t) = mt + b`

`-420 = 8m + b`

From the first equation:

`b = -320 - 3m`

So

`-420 = 8m + b`

`-420 = 8m - 320 - 3m`

`5m = -100`

`m = (-100)/(5)`

`m = -20`

And

`b = -320 - 3*(-20) = -260`

So

`d(t) = -20t - 260`