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# Example – the coffee cooling problem

Suppose you get a cup of coffee at a coffee shop. Should you mix the cream into the coffee at the shop or wait until you reach your office? The goal, we assume, is to have the coffee as hot as possible. So, the main question is how the coffee is going to cool as you walk back to the office.

The difference between the two strategies of mixing cream is:

• If you pour the cream at the shop, there is a sudden drop of temperature before the coffee starts to cool down as you walk back to the office
• If you pour the cream after getting back to the office, the sudden drop occurs after the cooling period during the walk

We need a model for the cooling process. The simplest such model is Newton's cooling law, which states that ...

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