A constant flow of water, 30 lbm/s, enters a cylindrical container from the top. At the bottom, an opening allows water to drain out at a rate, in lbm/s, that is proportional to H(t), the instantaneous height of water in the barrel, in ft: rate of water leaving from bottom = 9*H(t) . The circular base of the cylindrical container has an area of 3 ft^2 and the density of water is 62.4 lbm/ft^3. If the barrel is initially empty, plot the height of the water in the container as a function of time and explain the main features of the plot.