I would like to make sure the way I am solving this problem is correct...:
In a murder investigation, the temperature of the corpse was 32.5 degrees Celsius at 1:30 PM and 30.3 degrees Celsius an hour later. Normal body temperature is 37.0 degrees Celsius and the temperature of the surroundings was 20.0 degrees Celsius. When did the murder take place?
Ok, so here is where I'll start:
dT/dt = k(20-T)
dT/(20-T) = kdt
ln(20-T) = kt + c
20-T = Ce^kt ( C = e^c)
My initial conditions are:
T(0) = 37.0 degrees Celsius
T(t) = 32.5 degrees Celsius (t *which is time* would be the time when the murder took place)
T(t+1) = 30.3 degrees Celsius (one hour after the murder took place)
Is this the correct way to solve this problem? Of course I didn't finish because I would like to check if I have done everything correct first. It would be a great help if you answered
In a murder investigation, the temperature of the corpse was 32.5 degrees Celsius at 1:30 PM and 30.3 degrees Celsius an hour later. Normal body temperature is 37.0 degrees Celsius and the temperature of the surroundings was 20.0 degrees Celsius. When did the murder take place?
Ok, so here is where I'll start:
dT/dt = k(20-T)
dT/(20-T) = kdt
ln(20-T) = kt + c
20-T = Ce^kt ( C = e^c)
My initial conditions are:
T(0) = 37.0 degrees Celsius
T(t) = 32.5 degrees Celsius (t *which is time* would be the time when the murder took place)
T(t+1) = 30.3 degrees Celsius (one hour after the murder took place)
Is this the correct way to solve this problem? Of course I didn't finish because I would like to check if I have done everything correct first. It would be a great help if you answered