A commercial bakery uses an automated flour silo. The mass of the flour in the silo, F, in… — SAT

A commercial bakery uses an automated flour silo. The mass of the flour in the silo, $F$ , in kilograms, is modeled as a linear function of the time $t$ , in hours, after the bakery opens. The table below shows the mass of the flour remaining in the silo at two different times during the day:

Time (hours), $t$	Mass of flour (kilograms), $F$
$3$	$1,850$
$7$	$1,490$

If the mass of the flour in the silo decreases at a constant rate of $r$ kilograms per hour, what is the value of $r$ ?

Cevap: 90 kilograms per hour

Cevap

The rate of decrease of the flour is represented by the magnitude of the slope of the linear relationship. Using the points

(3, 1850)

and

(7, 1490)

from the table, the slope is calculated as

\frac{1490 - 1850}{7 - 3} = \frac{-360}{4} = -90

. This indicates that the mass of the flour decreases by

90

kilograms per hour. Therefore, the value of

r

90

Adım Adım Çözüm

Identify the data points representing time and mass from the table.

(t_1, F_1) = (3, 1850)

and

(t_2, F_2) = (7, 1490)

We need two coordinates to find the slope of the linear relationship.

Calculate the slope (rate of change) of the linear function.

Slope =

\frac{1490 - 1850}{7 - 3} = -90

The slope formula

\frac{y_2 - y_1}{x_2 - x_1}

gives the rate of change of the mass of the flour per hour.

Determine the value of

r

based on the rate of decrease.

r = 90

The rate of decrease is the positive magnitude of the rate of change.

Anahtar Kavram

Interpreting rate of change (slope) from tabular data in a linear context

Tahmini Süre:1m 30s

Soru

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Konular

Bu konudan daha fazla soru