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## Homework Statement

The coffee in a cup is at a temperature T(to) when t=to in a room that has temperature T1=20 degrees Celsius. The temperature of the coffee is found using the function:

[tex] T(t) = (T(t_0) - T_1) e^{(-\frac{t-t_0}{10})} + T_1 , t >= t_0 [/tex]

We add milk, so that the cup contains 90% aforementioned coffee and 10% milk. We are given that T(to) = 100 degrees and that we plan to drink the coffee at t=10. Refrigerated milk has 5 degree temperature. What's the best moment to add the milk so that when we decide to drink our coffee it has the highest possible temperature??

## Homework Equations

[tex] T(t) = (T(t_0) - T_1) e^{(-\frac{t-t_0}{10})} + T_1 , t >= t_0 [/tex]

## The Attempt at a Solution

There are reasons why I'm having trouble figuring my way through the problem, and mostly it's because I haven't ever dealt with temperature of a mixture of liquids. I know that I must construct a function of time that should produce max at t=10 but that is not all. Is it correct to consider that temperature of the cup will be 0.9 T(t) and 0.1 * 5, like a friend proposed? I would very much appreciate a hint, thanks!

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