I got a Guinness can whose temperature is 21°C. To enjoy it cold at the perfect temperature of 9°C, I set my refrigerator to 0°C. The temperature \( T(t) \) of the can at time \( t \) measured in seconds satisfies Newton’s Cooling Law equation:\[\frac{dT}{dt} = -0.0001T.\]How long will it take for the can to cool off to 9°C?

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Answered: I got a Guinness can whose temperature…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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At 7 pm on a Wednesday evening. Mr Huxley's water tank was full. The capacity of the tank was 3 000 litres. Unfortunately, the tap on the tank was leaking in such a way that the change in volume at any time (r) hours was proportional to the volume (V) of the tank. This means that AP =-kV . dt Show that V= Ve is a solution of this equation. Given that the volume of the tank after 3 hours is 1900 litres, show that k = 0.1523 correct to 4 decimal places. (iii) By the time Mr Huxley discovered that the tank was leaking, there were only 250 litres of water remaining. At what time and on which day did Mr Huxley discover the leak (Answer correct to the nearest minute)?
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