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An iceberg floating in the North Pacific Ocean weighs 80 metric tons. Each month it loses 5 metric tons of weight. Let
W be the weight in metric tons of the iceberg after
t months have passed. Which of the following best explains the relationship between
t and
W ?
Choose 1 answer:
(A) The relationship is exponential because
W is multiplied by a factor of 30 each time
t increases by 1 .
(B) The relationship is exponential because
W is multiplied by a factor of 0.3 each time
t increases by 1 .
C) The relationship is linear because
W decreases by 5 each time
t increases by 1 .
(D) The relationship is linear because
W always decreases as values of
t increase.

An iceberg floating in the North Pacific Ocean weighs $80$ metric tons. Each month it loses $5$ metric tons of weight. Let $W$ be the weight in metric tons of the iceberg after $t$ months have passed. Which of the following best explains the relationship between $t$ and $W$ ? $\newline$ Choose $1$ answer: $\newline$ (A) The relationship is exponential because $W$ is multiplied by a factor of $30$ each time $t$ increases by $1$ . $\newline$ (B) The relationship is exponential because $W$ is multiplied by a factor of $0$ . $3$ each time $t$ increases by $1$ . $\newline$ C) The relationship is linear because $W$ decreases by $5$ each time $t$ increases by $1$ . $\newline$ (D) The relationship is linear because $W$ always decreases as values of $t$ increase.

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Evaluate two-variable equations: word problems

Full solution

Q. An iceberg floating in the North Pacific Ocean weighs

80

metric tons. Each month it loses

5

metric tons of weight. Let

W

be the weight in metric tons of the iceberg after

t

months have passed. Which of the following best explains the relationship between

t

and

W

?

\newline

Choose

1

answer:

\newline

(A) The relationship is exponential because

W

is multiplied by a factor of

30

each time

t

increases by

1

.

\newline

(B) The relationship is exponential because

W

is multiplied by a factor of

0

.

3

each time

t

increases by

1

.

\newline

C) The relationship is linear because

W

decreases by

5

each time

t

increases by

1

.

\newline

(D) The relationship is linear because

W

always decreases as values of

t

increase.

Initial Weight and Monthly Loss: The iceberg starts at $80$ metric tons and loses $5$ metric tons each month.
Calculation of Weight After $t$ Months: To find the weight of the iceberg after $t$ months, we subtract $5t$ from the initial weight. $\newline$ $W = 80 - 5t$
Characteristics of Linear Relationship: This equation shows a constant change in weight for each increase in time, which is characteristic of a linear relationship.
Correct Answer Explanation: Therefore, the correct answer is (C) The relationship is linear because $W$ decreases by $5$ each time $t$ increases by $1$ .

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\newline

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Question

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