Air enters a tank through an area of \(0.018 \mathrm{~m}^{2}\) with a velocity of \(4.6 \mathrm{~m} / \mathrm{s}\) and a density of \(15.5 \mathrm{~kg} / \mathrm{m}^{3}\). Air leaves with a velocity of \(1.5 \mathrm{~m} / \mathrm{s}\) and a density equal to that in the tank. The initial density of the air in the tank is \(10.3 \mathrm{~kg} / \mathrm{m}^{3}\). The total tank volume is \(0.6 \mathrm{~m}^{3}\) and the exit area is \(0.04 \mathrm{~m}^{2}\). Find the initial rate of change of density in the tank.