I have a question that goes as follows:
For this question, assume that turkeys follow Newton’s law of cooling/heating. I start my oven heating at 12pm. The temperature of the oven increases linearly with time until it reaches 150C at 12.30pm. The oven is initially at room temperature, 20C.
a. Write an equation for the temperature of the oven as a function of t, the time in hours since 12pm.
b. A turkey is placed in the oven at 12pm. The relaxation time of the turkey is 1 hour. (Hint: this means that the constant in Newton’s law is ± 1/hour depending on your sign convention). The temperature of the turkey at 12pm is 4◦C. Find the temperature of the turkey at 12.30pm (leave powers of $e$ as part of your answer).
I know the question for this answer but I am having trouble doing the problem without it given that I cant quite associate the separate objects together. It seems that this is a general problem for me with differential equations, which is that I am really struggling to come up with an equation for some word problem that is given while, on the other hand, solving it afterwards is not really much of a problem. The most annoying thing is that I don't seem to see many practical application problems in textbooks (especially the one I am using).
Could someone offer up some advice for this problem and in general please ?
Thank you