Question

A submarine is at the surface of the ocean. It begins its descent at a rate of 100 feet per minute. Write a linear model in the form d(t)=mt+b where d(t) represents the depth of the submarine relative to sea level, in feet, after t minutes into its descent. Be sure to include "d(t) =" in your answer. (Note: when the submarine is below sea level, its depth is a negative quantity)

Answer 1

d(t) = -100t

Explanation:

The general expression for the linear model is:

`d(t)=mt+b`

Since the submarine already starts at sea level, b=0:

`d(t)=mt`

The constant "m" is the rate at which the submarine descends in feet per minute. Considering depth as a negative quantity, m=-100

`d(t)=-100t`

The linear model that represents the depth of the submarine relative to sea level, in feet, after t minutes is d(t) = -100t.