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Zorluk: OrtaInterpreting Linear Relationships in Context

A researcher monitors the temperature of a chemical compound during an experiment. The temperature, TT, in degrees Celsius, of the compound mm minutes after heating begins can be modeled by a linear relationship. The temperature increases by 4.54.5 degrees Celsius every 22 minutes. If the temperature of the compound was −12-12 degrees Celsius when heating began, after how many minutes will the temperature of the compound reach 1515 degrees Celsius?

Cevap: 12 minutes

Cevap

The temperature of the compound will reach 1515 degrees Celsius after 1212 minutes.
The correct answer is 1212 because the temperature increases at a constant rate of 2.252.25 degrees Celsius per minute. Starting from an initial temperature of −12-12 degrees Celsius, the equation is T=2.25m−12T = 2.25m - 12. Setting T=15T = 15 gives 15=2.25m−1215 = 2.25m - 12, which simplifies to 27=2.25m27 = 2.25m, resulting in m=12m = 12.

Adım Adım Çözüm

1
Calculate the constant rate of temperature increase per minute.
2.252.25 degrees Celsius per minute
This rate represents the slope of the linear relationship between time and temperature.
2
Formulate the linear equation representing the temperature TT as a function of the elapsed minutes mm.
T=2.25m−12T = 2.25m - 12
The slope is 2.252.25 and the vertical intercept is the initial temperature of −12-12 degrees Celsius.
3
Set T=15T = 15 and solve the linear equation for mm.
m=12m = 12
This determines the exact number of minutes needed for the temperature to reach 1515 degrees Celsius.

Anahtar Kavram

Interpreting and solving linear equations modeled from context
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Interpreting Linear Relationships in Context

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