A researcher monitored the mass of a cooling block of metal over time as it underwent subl… — SAT

A researcher monitored the mass of a cooling block of metal over time as it underwent sublimation in a vacuum chamber. The table below shows the mass of the metal block, $M$ , in grams, for several values of time, $t$ , in hours after the sublimation process began.

Time, $t$ (hours)	Mass, $M$ (grams)
$2$	$112.4$
$5$	$104.6$
$8$	$96.8$

If the relationship between $M$ and $t$ is linear, which of the following is the best interpretation of the slope of the graph of this relationship in the $tM$ -plane?

The mass of the metal block decreases by $2.6$ grams each hour.Cevap
B
The initial mass of the metal block before sublimation began was $117.6$ grams.
C
The mass of the metal block decreases by $7.8$ grams each hour.
D
The mass of the metal block after $1$ hour of sublimation is $115.0$ grams.

Cevap

The mass of the metal block decreases by

2.6

grams each hour.

The correct answer is the option stating that the mass of the metal block decreases by

2.6

grams each hour. The slope of a linear model is the rate of change, which is computed as the change in the dependent variable divided by the change in the independent variable. Here,

\frac{104.6 - 112.4}{5 - 2} = -2.6

, representing a change of

-2.6

grams per hour.

Adım Adım Çözüm

Calculate the slope of the linear relationship using two points from the table.

Using the points

(2, 112.4)

and

(5, 104.6)

, the slope is

\frac{104.6 - 112.4}{5 - 2} = \frac{-7.8}{3} = -2.6

The slope represents the constant rate of change of the dependent variable (

M

) per unit change in the independent variable (

t

Interpret the calculated slope value in the context of the problem.

A slope of

-2.6

means that the mass

M

decreases by

2.6

grams for every

1

hour increase in time

t

The negative sign indicates a decrease, and the rate is expressed in units of the dependent variable per unit of the independent variable (grams per hour).

Anahtar Kavram

Interpreting the slope of a linear relationship in context.

Tahmini Süre:1m 30s

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