question archive We recall Newton's law of cooling
Subject:MathPrice: Bought3
We recall Newton's law of cooling. If E is the ambient temperature and T = T(t) is the temperature of an object at time t, then the rate of change of T is proportional to the temperature difference. That is, T(t) satisfies the differential equation
(1). dT/dt = k(E − T)
(a) [3 points] Verify that the function (2).T(t) = E + (T0 − E)e −kt
satisfies equation (1), assuming that the ambient temperature E is constant. (It is a fact that, up to the value of T0, this is the only solution to (1) when E is constant.)