A coffee roasting company uses a commercial roasting machine. The temperature of the roast… — SAT

A coffee roasting company uses a commercial roasting machine. The temperature of the roasting drum, $T$ , in degrees Fahrenheit ( $^\circ\text{F}$ ), is modeled as a linear function of the roasting time, $t$ , in minutes, where $0 \leq t \leq 10$ . After $2$ minutes of roasting, the temperature of the drum is $280^\circ\text{F}$ . After $5$ minutes of roasting, the temperature of the drum is $385^\circ\text{F}$ . What is the rate of temperature increase, in degrees Fahrenheit per minute, of the roasting drum?

Cevap: 35 degrees Fahrenheit per minute

Cevap

The rate of temperature increase of the roasting drum is

35

degrees Fahrenheit per minute.

The temperature,

T

, is modeled as a linear function of time,

t

. The constant rate of temperature increase corresponds to the slope of this linear function. Given two points,

(2, 280)

and

(5, 385)

, the slope is calculated as the change in temperature divided by the change in time:

\frac{385 - 280}{5 - 2} = \frac{105}{3} = 35

degrees Fahrenheit per minute.

Adım Adım Çözüm

Identify the coordinates representing the relationship between time and temperature.

The two points are

(2, 280)

and

(5, 385)

, where the first coordinate is the time,

t

, in minutes, and the second coordinate is the temperature,

T

, in degrees Fahrenheit.

To find the rate of change of a linear relationship, we first need to determine two points

(t_1, T_1)

and

(t_2, T_2)

from the given context.

Calculate the rate of temperature increase as the slope of the line passing through these two points.

The slope

m

is given by

m = \frac{385 - 280}{5 - 2} = \frac{105}{3} = 35

The rate of temperature increase per minute is the constant slope of the linear relationship.

Anahtar Kavram

Slope of a linear relationship in context

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