Is thermal equilibrium possible by the Law of Cooling?

samedi 31 août 2013

Law of cooling states that the rate of loss of heat by a body is directly proportional to the excess temperature of the body above that of its surroundings. The equation of determining temperature in time T(t)=Ta+(T0-Ta)*e^kt (Ta-ambient temperature, T0-initial temperature, k-heat transfer constant) is a standart example of exponential decay BUT I don't understand the fact that in this equation ambient temperature in a graph is a horizontal asymptote, and If im not wrong, then the graph goes to infinity never reaching this point. That means the object which is cooling down never actually reaches temperature of the surroundings therefore thermal equilibrium is not reached (also remembering that ambient temperature is all the way a constant). How is that possible?

Thank you!