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A tank holding 600 liters of milk is leaking. Each week it loses 60 liters of milk. Let
M be the number of liters of milk remaining in the tank after leaking for
t weeks. Which of the following best explains the relationship between
t and
M ?
Choose 1 answer:
(A) The relationship is linear because
M always decreases as values of
t increase.
(B) The relationship is exponential because
M decreases by 60 each time
t increases by 1 .
(C) The relationship is exponential because
M is multiplied by a factor of 0.6 each time
t increases by 1 .
(D) The relationship is linear because
M decreases by 60 each time
t increases by 1 .

A tank holding $600$ liters of milk is leaking. Each week it loses $60$ liters of milk. Let $M$ be the number of liters of milk remaining in the tank after leaking for $t$ weeks. Which of the following best explains the relationship between $t$ and $M$ ? $\newline$ Choose $1$ answer: $\newline$ (A) The relationship is linear because $M$ always decreases as values of $t$ increase. $\newline$ (B) The relationship is exponential because $M$ decreases by $60$ each time $t$ increases by $1$ . $\newline$ (C) The relationship is exponential because $M$ is multiplied by a factor of $0$ . $6$ each time $t$ increases by $1$ . $\newline$ (D) The relationship is linear because $M$ decreases by $60$ each time $t$ increases by $1$ .

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Evaluate two-variable equations: word problems

Full solution

Q. A tank holding

600

liters of milk is leaking. Each week it loses

60

liters of milk. Let

M

be the number of liters of milk remaining in the tank after leaking for

t

weeks. Which of the following best explains the relationship between

t

and

M

?

\newline

Choose

1

answer:

\newline

(A) The relationship is linear because

M

always decreases as values of

t

increase.

\newline

(B) The relationship is exponential because

M

decreases by

60

each time

t

increases by

1

.

\newline

(C) The relationship is exponential because

M

is multiplied by a factor of

0

.

6

each time

t

increases by

1

.

\newline

(D) The relationship is linear because

M

decreases by

60

each time

t

increases by

1

.

Define initial amount: First, let's define the initial amount of milk in the tank, which is $600$ liters.
Calculate amount lost: Next, we know the tank is losing $60$ liters of milk each week. So, if $t$ represents the number of weeks, the amount of milk lost after $t$ weeks is $60$ liters multiplied by $t$ .
Find remaining milk: Now, to find the remaining milk $M$ after $t$ weeks, we subtract the amount lost from the initial amount. So, $M = 600 - (60 \times t)$ .
Constant rate of change: This equation shows that for every increase in $t$ by $1$ week, $M$ decreases by $60$ liters. This is a constant rate of change.
Linear relationship explanation: Since the rate of change is constant, the relationship between $t$ and $M$ is linear, not exponential. Exponential relationships involve percentages or factors, not constant subtraction.
Correct answer explanation: Therefore, the correct answer is (D) The relationship is linear because $M$ decreases by $60$ each time $t$ increases by $1$ .

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\newline

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\newline

1

\newline

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Question

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1

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