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.