Could someone please tell me what the "exponential law of cooling" might be.
The "law" states that an object approaches the temperature of its
surroundings at a rate which is exponential in time. If The initial
temperature of the object is Ti and the temperature of the surroundings
is To, the temperature varies with time according to
T(t) = To + (Ti-To) exp (-t/tau)
where tau is the time constant for the approach to equilibrium. The
"law" is not highly accurate because the conditions under which it
would be appropriate are not approached often; it lacks generality.
Qualitatively the time dependence is reasonable, however.