Write the differential equation expressing the hypothesis that the rate of change of a temperature is proportional to the temperature T.  Evaluate the proportionality constant if it is known that the when the temperature is 3709 its rate of change is known to be 500.   If this is the t=0 state of the temperature, then approximately what will be the temperature at t = 1.8?  What then will be the temperature at t = 3.6?