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Difficulty: MediumInterpreting Linear Relationships in Context

A specialized cooling system is used to lower the temperature of a chemical solution in a laboratory. The temperature of the solution, TT, in degrees Celsius, can be modeled by the linear equation T=85.4−1.25mT = 85.4 - 1.25m, where mm is the number of minutes since the cooling process began. According to the model, how many minutes does it take for the temperature of the solution to decrease by 1515 degrees Celsius?

Answer: 12 minutes

Answer

12 minutes
The correct answer is 12. In the equation T=85.4−1.25mT = 85.4 - 1.25m, the coefficient of mm is −1.25-1.25, which indicates that the temperature decreases by 1.251.25 degrees Celsius for each minute that passes. To find how many minutes it takes for the temperature to decrease by 1515 degrees Celsius, divide the total decrease by the rate of decrease: 151.25=12\frac{15}{1.25} = 12.

Step-by-Step Solution

1
Identify the rate of change from the linear equation.
The rate of decrease is 1.251.25 degrees Celsius per minute.
The slope of the linear equation T=85.4−1.25mT = 85.4 - 1.25m is −1.25-1.25, representing the change in temperature per minute.
2
Divide the target temperature change by the rate of change to find the time.
12 minutes
To find the number of minutes for a 1515-degree decrease at a rate of 1.251.25 degrees per minute, calculate 151.25\frac{15}{1.25}.

Key Concept

Interpreting the slope of a linear relationship in context
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Topics

Interpreting Linear Relationships in Context

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