Desperate help in newton’s law cooling

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I’m a high school student that is attempting to explore the math involved behind newton’s law of cooling. I have tried to derive the equation and the idea was to apply it to a crime scene and finding the values of change in temperature and time. I talked to my teacher about this math exploration for her opinion on the difficulty of the math involved. Her answer was it is quite simple and I should integrate more math that maybe a bit more difficult that should be within my level of mathematics which in this case is higher math but the problem is I have no clue what else could be added into this law. In conclusion, if it would be possible to give me inspiration of what math I could involve that might be slightly harder than just deriving the equation to make my explorations slightly more difficult but stay within the difficulty of a high school student.