Oil is being pumped continuously from a certain oil well at a rate proportional to the amount of oil left in the well; that is dy/dt = ky, where is the amount of oil left in the well at any time t. Initially there were 1.000.000 gallons of oil in the well, and 6 years later there were 500.000 gallons remaining. It will no longer be profitable to pump oil when there are fewer than 50.000 gallons remaining.
Write an equation for y, the amount of oil remaining in the well at any time t