3) The mathematical formulation of Newton's empirical law of warming of an object is given by the linear first-order differential equation dT kT = −kTm dt dT or = k(T - Tm) dt where k is a constant of proportionality, T(t) is the temperature of the object for t > 0, and Tm is the ambient temperature- that is, the temperature of the medium around the object. Applying above law to solve the following problem: A thermometer is removed from a room where the temperature is 20°C and is taken outside, where the air temperature is 34°C. After 1 minute the thermometer reads 24°C. What is the reading of the thermometer at t = 2 min? How long will it take for the thermometer to reach 30°C?

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