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

Answer:

d(t)=-100t

Step-by-step explanation:

d is the independent variable and t is the dependent variable. The rate of descent has to be negative so that the altitude decreases compared to sea level. The initial sea level is 0.

Answer 2

Answer:

d(t) = -100t

Step-by-step 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.