Question

# If a cup of coffee has temperature 100°C in a room where the ambient air temperature...

If a cup of coffee has temperature 100°C in a room where the ambient air temperature is 21°C, then, according to Newton's Law of Cooling, the temperature of the coffee after t minutes is T ( t ) = 21 + 79 e − t / 45 . What is the average temperature of the coffee during the first 14 minutes?

we have equation for temperature as

we have to find average temperature in first 14 min

Firstly, we will find integral

we can solve each integrals and then combine them

now, we can find average value

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