Extraordinary Differential Equations #11

Calculus Level 3

Newton's Law of Cooling states that the rate at which a hot object cools down is directly proportional to the temperature difference between itself and its environment.

Suppose an object at \(100.0^{\circ} \text{C}\) is left to cool down in an environment of a fixed lower ambient temperature. If the object's temperature is \(80.0^{\circ} \text{C}\) after an hour, and \(54.6^{\circ} \text{C}\) after another 2 hours, calculate the ambient temperature of the surrounding temperature in \(^{\circ} \text{C}\).

(This problem is part of the set Extraordinary Differential Equations.)

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