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## Homework Statement

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.

## Homework Equations

That one

## 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?