Question

If a cup of coffee has temperature 95∘C in a room where the temperature is 20∘C, then, according to Newton's Law of Cooling, the temperature of the coffee after t minutes is

T(t)=20+75e^(−t/50).
What is the average temperature (in degrees Celsius) of the coffee during the first half hour?

Average temperature =

Answer 1

as usual, the average value over the 30-minute interval is

1/30 ∫[0,30] 20+75e^(−t/50) dt = 76,40