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A block of ice weighing 100 kilograms begins to melt. Each hour the block of ice loses
5% of its weight. Let
W be the weight, in kilograms, of the block of ice after melting for
t hours. 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 0.95 each time
t increases by 1 .
(B) The relationship is linear because
W is multiplied by a factor of
5% each time
t increases by 1 .
(C) The relationship is linear because
W decreases by 5 as
t increases from
t=0 to
t=1.
(D) The relationship is exponential because
W decreases by 9.75 as
t increases from
t=0 to
t=2.

A block of ice weighing $100$ kilograms begins to melt. Each hour the block of ice loses $5 \%$ of its weight. Let $W$ be the weight, in kilograms, of the block of ice after melting for $t$ hours. 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 $0$ . $95$ each time $t$ increases by $1$ . $\newline$ (B) The relationship is linear because $W$ is multiplied by a factor of $5 \%$ each time $t$ increases by $1$ . $\newline$ (C) The relationship is linear because $W$ decreases by $5$ as $t$ increases from $t=0$ to $t=1$ . $\newline$ (D) The relationship is exponential because $W$ decreases by $9$ . $75$ as $t$ increases from $t=0$ to $t=2$ .

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Evaluate two-variable equations: word problems

Full solution

Q. A block of ice weighing

100

kilograms begins to melt. Each hour the block of ice loses

5 \%

of its weight. Let

W

be the weight, in kilograms, of the block of ice after melting for

t

hours. 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

0

.

95

each time

t

increases by

1

.

\newline

(B) The relationship is linear because

W

is multiplied by a factor of

5 \%

each time

t

increases by

1

.

\newline

(C) The relationship is linear because

W

decreases by

5

as

t

increases from

t=0

to

t=1

.

\newline

(D) The relationship is exponential because

W

decreases by

9

.

75

as

t

increases from

t=0

to

t=2

.

Initial Weight Calculation: The initial weight of the ice block is $100\,\text{kg}$ . Each hour, it loses $5\%$ of its weight. To find the weight after $t$ hours, we need to apply the percentage decrease repeatedly for each hour.
Weight Decrease Calculation: The weight after $1$ hour would be $100 \, \text{kg} \times (1 - 0.05) = 100 \, \text{kg} \times 0.95$ .
Exponential Relationship Explanation: After $2$ hours, the weight would be $100 \, \text{kg} \times 0.95 \times 0.95$ . This shows that the weight is multiplied by $0.95$ for each hour that passes, which is an exponential relationship.
Option (A) Explanation: Option (A) states that the relationship is exponential because $W$ is multiplied by a factor of $0.95$ each time $t$ increases by $1$ . This matches our calculation.
Option (B) Explanation: Option (B) is incorrect because a linear relationship would imply that the weight decreases by the same amount each hour, not by a percentage.
Option (C) Explanation: Option (C) is incorrect because $W$ does not decrease by a constant $5$ kg each hour; it decreases by $5\%$ of the remaining weight.
Option (D) Explanation: Option (D) is incorrect because it states that $W$ decreases by $9.75\,\text{kg}$ as $t$ increases from $t=0$ to $t=2$ , which is not how the percentage decrease works.

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