where is the room temperature.
This gives that
If we seperate this equation and integrate we getwe get that
We are told the temperature at midnight and 30 minutes later
Using these two data point we get
puting the first equation into the 2nd gives
Puting this back into the orginial equation gives
Solving this for time gives
Since we know the temperature of the body at midnight we can plug that into this equation to get
Now if you plug in the two initial temperatures it will give you the number of minutes before midnight. Just use the two different values of given.