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suppose you make a coffee and it starts off just too hot to drink so you put it in the refrigerator temporarily to cool it off. if the original temperature is 190 degrees fahrenheit and the refrigerator is 36 degrees fahrenheit what will the temperature of the coffee be after 3 minutes? (k=0.12)

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Answer:

After 3 minutes in the refrigerator, the temperature of the coffee will be approximately 89.6 degrees Fahrenheit

Explanation:

To solve this problem, we can use Newton's law of cooling, which states that the rate of change in the temperature of an object is proportional to the difference between its temperature and the temperature of its surroundings. The equation for Newton's law of cooling is:

T(t) = T_s + (T_0 - T_s) * e^(-kt)

Where:

T(t) is the temperature of the object at time t

T_s is the temperature of the surroundings

T_0 is the initial temperature of the object

k is the cooling constant

e is the base of the natural logarithm

In this case, we have:

T_s = 36 degrees Fahrenheit (temperature of the refrigerator)

T_0 = 190 degrees Fahrenheit (initial temperature of the coffee)

k = 0.12 (cooling constant)

t = 3 minutes (time elapsed)

Substituting these values into the equation, we get:

T(3) = 36 + (190 - 36) * e^(-0.12*3)

T(3) = 36 + 154 * e^(-0.36)

T(3) ≈ 89.6 degrees Fahrenheit

Therefore, after 3 minutes in the refrigerator, the temperature of the coffee will be approximately 89.6 degrees Fahrenheit.

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