NEED HELP ON PRECAL HW ASAP!!!

Question

A pizza pan is removed at 8:00PM from an oven whose temperature is fixed at 425F into a room that is a constant 74F After 5​ minutes, the pizza pan is at 300F ​(a) At what time is the temperature of the pan ​(b) Determine the time that needs to elapse before the pan is ​(c) What do you notice about the temperature as time​ passes?

Answer 1

Cooling is an exponential decay with the limit as time approaches infinity as the ambient temperature (aka room temp).

Generically it goes like this T(t) = ΔT(r)^t + T_amb where T is the temperature at any time "t", ΔT is the difference between the initial temp and the ambient temp, and "r" is the cooling rate.

So, in this case, the initial temp is 425° (we're assuming the pizza got up to the oven temp when it was cooking) and the room or ambient temp is 74. So the ΔT is 425 - 74 = 351. So our equation is:

T(t) = 351(r)^t + 74 but we need to find "r". To do so, use the data point that was given. After 5 minutes the temp was 300. Plugging that in we get:

300 = 351(r)⁵ + 74

300 - 74 = 351(r)⁵

226/351 = r⁵

r = 5th root or 0.6438746439 or r = 0.9157148656

So our equation is then:

T(t) = 351(0.9157148656)^t + 74

Using this equation you can solve for the questions asked.