Write the differential equation expressing the hypothesis that the rate of change of a population is proportional to the population P.  Evaluate the proportionality constant if it is known that the when the population is 2174 its rate of change is known to be 200.   If this is the t=0 state of the population, then approximately what will be the population at t = 1.6?  What then will be the population at t = 3.2?