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Use Newton's Law of Cooling to find the temperature of a substance as a function of time (

t in minutes). The cooling relationship is given by
y=2 t+a, where
y is the temperature of the medium surrounding the cooling object,
a is the difference between the initial temperature of the object and the surrounding temperature, and
k is a constant related to the cooling object.

a. Find the first sample's temperature after it has cooled for 20 minutes.

User Makarius
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Final answer:

The student's question involves finding the temperature of a substance after 20 minutes using a simplified form of Newton's Law of Cooling. However, without the constant 'k' or the initial temperature difference 'a', it's not possible to provide a unique solution.

Step-by-step explanation:

To find the temperature of a substance as a function of time using Newton's Law of Cooling, we interpret the given relationship y=2t+a. In this context, 'y' stands for the temperature of the medium surrounding the cooling object, 'a' represents the difference between the initial temperature of the object and the surrounding temperature, and 'k' is a constant related to the cooling object. However, k is not used in the provided expression, which suggests the relationship may be a simplified version of the law or misstated, as typically Newton's Law of Cooling is represented as an exponential decay over time.

To find the temperature after 20 minutes, replace 't' with 20 in the equation to get y=2(20)+a, simplifying to y=40+a.

Without the value of 'a' or additional context that provides the cooling rate constant 'k' or initial conditions, the temperature at 20 minutes cannot be uniquely determined. Newton's Law of Cooling in its full form would need these to calculate the temperature at any given time.

User Veeman
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