If you remove a glass of iced tea from the refrigerator, and leave it sitting on the table
in a room with temperature 25 C, then Newton’s Law of Temperature Change gives
the temperature of the tea after t minutes as
f(t) = 25 − Ce−kt
where C and k are constants. Show that the rate of change of f(t) is proportional to
the difference between the temperature of the tea, and that of the room, at every time t.
The Attempt at a Solution
OK I know the rate of change is the derivative. So f'(t) = Cke-kt right? But how am I supposed to show that f'(t) is proportional to the difference mathematically?