Explanation:
According to Newton's law of cooling,
![T(t)=T_s+(T_o-T_s){e^{{-t/\tau}}](https://tex.z-dn.net/?f=T%28t%29%3DT_s%2B%28T_o-T_s%29%7Be%5E%7B%7B-t%2F%5Ctau%7D%7D)
T(t) is the temperature at time t
is temperature of surrounding
![k=\dfrac{1}{\tau}](https://tex.z-dn.net/?f=k%3D%5Cdfrac%7B1%7D%7B%5Ctau%7D)
At the time of discovery, the temperature of the dead body was, ![T_o=36^{\circ}C](https://tex.z-dn.net/?f=T_o%3D36%5E%7B%5Ccirc%7DC)
Temperature of the surrounding, ![T_s=24^{\circ}C](https://tex.z-dn.net/?f=T_s%3D24%5E%7B%5Ccirc%7DC)
Temperature after 4 hours, ![T=30^{\circ}C](https://tex.z-dn.net/?f=T%3D30%5E%7B%5Ccirc%7DC)
So, ![30=24+(36-24)e^{-4t}](https://tex.z-dn.net/?f=30%3D24%2B%2836-24%29e%5E%7B-4t%7D)
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
![37=24+(36-24)e^{0.17t}](https://tex.z-dn.net/?f=37%3D24%2B%2836-24%29e%5E%7B0.17t%7D)
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.