Question:
A fast food restaurant wants a special container to hold coffee. the restautrant wishes the container to quickly cool the coffee from 200 degrees to 130 degrees fahrenheit and keep the liquid between 110 degrees and 130 degrees as long as possible. the restaurant has three containers to select from.
1. a container that reduces the temperature of the liquid from 200 degrees to 100 degrees Fahrenheit in 30 minutes by maintaining a container temperature of 70 degrees Fahrenheit.
2. a container that reduces the temperature of the liquid from 200 degrees to 110 degrees fahrenheit by maintaining a constant temperature of 60 degrees fahrenheit.
3. a container that reduces the temperature of the liquid from 200 degrees to 120 degrees fahrenheit by maintaining a constant temperature of 65 degrees fahrenheit.
1. which container must the restaurant choose?
2. How long does it take each container to lower the coffee temperature from 200 degrees fahrenheit to 130 degrees fahrenheit?
3. Using newton''s law of cooling, find a function relating the temperature of the liquid over time for each container.