After a few years of hard work, you have finally saved enough money to open your own coffee-shop. You wish to find a special container to quickly cool the coffee from 200 to 130 F and keep the liquid between 110 and 130 F for as long as possible. Your manager was able to find three container to select from.

Company 1 offers you a container that reduces the temperature of a liquid from 200F to 100F in 30 minutes by maintaining a constant temperature of 70F.

Company 2 has a container that reduces the temperature from 200F to 110F in 25 minutes by maintaining a constant temperature of 60F.

Company 3 sells a container that reduces the temperature from 200F to 120F in 20 minutes by maintaining a constant temperature of 65F.

Using Newton’s Law of Cooling to find a function that relating the temperature of the liquid over each container (bring your graphs to class). How long does it take for each container to to lower the temperature from 200F to 130F? How long will the coffee stay between 110F and 130F (optimal drinking temperature)? Which company would you choose and why? What other factors would you consider?

Newton’s Law of Cooling

The temperature of u of a heated object at a given time can be modeled by the following function *U(t)=T+(u*_{0 }–T)e^{kt} where *T* is the constant temperature of the surrounding medium, *u*_{0} is the initial temperature of the heated object, and *k* is a negative constant

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