Explanation:
According to Newton's law of cooling,
T(t) is the temperature at time t
is temperature of surrounding
At the time of discovery, the temperature of the dead body was,
Temperature of the surrounding,
Temperature after 4 hours,
So,
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
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.