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MATH IA HELP

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Soo, I did my IA based on Newton's law of cooling (for differential equations) and, although in the beginning my teacher said it was ok, now he told me that it is too simple and that I should somehow expand on it. 

Does anyone have an idea on how I could make it a bit more complex? Or perhaps something that I could add to make it more diverse?

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Consider the important/significance of the time constant. For example, if in one equation k = 1 and in another k = 2, just by how much is the k = 2 cooling faster?

What would be some limitations to this model? What considerations could make Newton's Law of Cooling more realistic?

If you have data, what would be an efficient method to find the time constant (with connections to HL functions units)?

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