The Newton law of cooling states that the temperature of the cup of coffee in the room is this function of time t


    T(t) =  = .


where "k" is the decay constant.  

At t= 13 minutes  T(t)= 50,  which gives you an equation to find the decay constant k:


    50 = 24 + 68*e^(-k*13)

    68*e^(-k*13) = 50 - 24 = 26

    e^(-13k) =  = 0.3823

    - 13k = ln(0.3823)

    k =  = 0.074.


Thus the decay constant k is found.


The last step is to find the time under the question. For it, you have this equation

    T(t) =  = 30

    e(-0.074*t) =  = 0.088

    -0.074*t = ln(0.088)

    t =  = 32.8


Answer. 32.8 minutes counting from the very beginning time moment.