# Newton's law of cooling to find time of death

by Lee.Robbo
Tags: cooling, death, exponential, help!, newton's law
 P: 308 What you've listed for Newton's law of cooling is actually not Newton's law of cooling. Rather, it is simply a solution of the actual law under the assumptions that ambient temperature is constant. Newton's law of cooling is actually: $$\frac{dT}{dt} = -k(T-T_e)$$ In order to solve it, you'll have to derive a function for $T_e = T_e(t)$ using the information given in the problem, and plug this function into the equation above. You'll have to solve the ODE to obtain $T(t)$.