differential equation?

Question

differential equations problem..


at 2:00 pm a thermometer reading 80 deg F is taken outside where the air temperature is 20 deg F. At 2:03 pm, the temperature reading yielded by the thermometer is 42 deg F.. Later the thermometer is brought inside where the air temperature 80 deg F.. At 2:10 pm, the temperature reading is 71 deg F. When was the thermometer brought indoors?

Answer 1

I can't give you a full answer but perhaps can give you some pointers to how it might be done. I think that we must assume that the rate of change of temperature is proportional to the difference between the thermometer temperature and the surrounding temperature. Using T for temperature shown and t for time this means dT/dt = k(20 - T) so negative when outside and the indicated temperature falls. It would be
dT/dt = k(80 - T) so positive when inside and the indicated temperature rises. Hope this is enough to get you started.