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Question

if a Cup of coffee has temperature 97°C in a room where the ambient air temperature is 24°C, then, according to newton’s law of cooling, The temperature of the coffee after T minutes is T(t)=24+73e^-t/50. What is the average temperature of the coffee during the first 10 minutes? Average Temp = ? °C

Answer 1

Average temperature is integral over interval:

[∫(24 + 73e^(-t/50) ) from 0 to 10]/(10-0) ≈ 90.163°C.