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

Answer:

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

Step-by-step 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

$-420 = 8m + b$

$-420 = 8m - 320 - 3m$

$5m = -100$

$m = \frac{-100}{5}$

$m = -20$

And

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

So

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