4. The Detective branch from the Dhaka Metropolitan Police has come to ask you for assistance on determining the time when a victim of crime has died. The dead body has been found in the freezer of a criminal hideout. Luckily, the manufacturer of the freezer has provided you the differential equation that can help you estimate the time of death from the temperature of the body. The differential equation is dT dT +8 + 167 = e(-2), dt2 dt where t represents the time in hours and T represents the temperature in Celcius. The initial temperature of the body is assumed to be the average human body temperature T(0) = 37°C. The manufacturer of the freezer has also informed you that the initial rate of decrease of temperature is T'(0) = -1°C/h. (a) Find T (t) using the initial conditions. (b) We already know from the initial conditions that the temperature at t = 0h is T(0) = 37°C. Find the temperature T of the body using part(a) for time t 1h, t 2h and t 3h (this will give you all the information you need to estimate the time of death). Given that, the temperature of the body is currently 6.3258°C, report the time of death between which hour to hour( for instance if the person has died between t 2h and t 3h, report from hour 2 to hour 3). Hint:You maybe able to use the fact that the temperature of the body in the freezer is always decreasing and never increasing (you do not need to solve any equation).