Explanation:
According to Newton's law of cooling,
[tex]T(t)=T_s+(T_o-T_s){e^{{-t/\tau}}[/tex]
T(t) is the temperature at time t
[tex]T_s[/tex] is temperature of surrounding
[tex]k=\dfrac{1}{\tau}[/tex]
At the time of discovery, the temperature of the dead body was, [tex]T_o=36^{\circ}C[/tex]
Temperature of the surrounding, [tex]T_s=24^{\circ}C[/tex]
Temperature after 4 hours, [tex]T=30^{\circ}C[/tex]
So, [tex]30=24+(36-24)e^{-4t}[/tex]
On solving the above equation,
k = 0.1735
Now, put the value of k in equation (1) at T = 36 degrees C
We know that, the temperature of body before death is T(t) = 37 degrees C
[tex]37=24+(36-24)e^{0.17t}[/tex]
On solving above equation,
t = -0.46 hour
As time can't be negative and we have taken 7:00 pm as reference time.
So, t = 27.67 minutes
So, the death of the person is at 6 : 32 pm. Hence, this is the required solution.