Final answer:
The rate at which the temperature of the coffee is changing can be determined using Newton's law of cooling. For this problem, the rate is approximately -0.574°F per degree of temperature difference.
Step-by-step explanation:
According to Newton's law of cooling, the rate at which the temperature of an object changes is directly proportional to the difference between the temperature of the object and that of the surrounding medium. In this case, the initial temperature of the coffee is 212°F and the temperature of the surrounding room is 76°F, so the temperature difference is 212°F - 76°F = 136°F. The final temperature of the coffee is 134°F. To find the rate at which the temperature of the coffee is changing, we can use the formula:
Rate of change of temperature = k * (difference in temperature)
where k is the constant of proportionality. We can plug in the values:
Rate of change of temperature = k * 136°F = (final temperature - initial temperature)
Plugging in the final temperature and initial temperature:
Rate of change of temperature = k * 136°F = 134°F - 212°F
Simplifying the equation:
k * 136°F = -78°F
Dividing both sides by 136°F:
k = -78°F / 136°F ≈ -0.574
Therefore, the rate at which the temperature of the coffee is changing is approximately -0.574°F per degree of temperature difference.