Final answer:
To determine the times when the pizza pan reaches specific temperatures, one would typically use an exponential decay equation related to Newton's law of cooling. Without further information like the rate of cooling, we cannot calculate the exact times. Over time, the temperature of the pan will approach the room temperature exponentially.
Step-by-step explanation:
The question involves the cooling of a pizza pan and the application of Newton's law of cooling to determine the time at which the temperature of the pan reaches certain values. While the precise mathematical model is not given in the question, the concept typically involves an exponential decrease in temperature over time.
(a) To find when the temperature of the pan reaches 135°F, one would usually set up an exponential decay equation based on the temperature at 5 minutes and solve for the time value when the temperature will be 135°F. However, without the rate of cooling, we cannot calculate the exact time.
(b) The same method is used to determine when the temperature of the pan is at 170°F. Again, the exact time cannot be calculated without the rate of cooling or an exponential decay equation.
(c) As time passes, the temperature of the pan approaches the ambient temperature of the room, 72°F, at a decreasing rate, indicating an exponential decay of the temperature difference.