Final answer:
To find the time at which the temperature of the pan is 135°F and the time needed for the pan to reach 150°F, set up proportions using the initial and final temperatures of the pan and the time elapsed. As time passes, the temperature of the pan decreases.
Step-by-step explanation:
To answer these questions, we can use the concept of thermal equilibrium, which states that when two objects with different temperatures come into contact, heat transfers between them until they reach the same temperature. In this case, we have a pizza pan that starts at 400°F and a room at 73°F.
(a) To find the time at which the pan is at 135°F, we can set up a proportion using the initial and final temperatures of the pan and the time elapsed. Let's denote the time as 't'. The proportion is: (400°F - 73°F)/(7:00 pm - t) = (300°F - 73°F)/(7:00 pm - 7:05 pm). We can solve this proportion to find the value of 't'.
(b) Similarly, to determine the time needed for the pan to reach 150°F, we can set up a proportion using the initial and final temperatures of the pan and the time elapsed: (400°F - 73°F)/(7:00 pm - t) = (150°F - 73°F)/(7:00 pm - ?). We can solve this proportion to find the time.
(c) As time passes, we can notice that the temperature of the pan decreases, moving towards the room temperature of 73°F.