Hi! Any help with this ODE word problem will be appreciated!
I'll simplify it to the important data:
We are keeping track of the temperature of coffee. Well, we have the temperature at two times and want a third. I would like to be able to conceptualize what's going on, if anyone can help!
7:30am \(200^\circ\text F\)
7:45am \(120^\circ\text F\)
8:00am \(?^\circ\text F\)
The rate of change of heat is a simplified version of Newton's Law of Cooling, that \(\dfrac{dT}{dt}=k(T-T_r)\) where \(k\) is a proportionality constant and \(T_r\) is the room temperature (\(70^\circ\text F\)).

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