The family of parabolas y = (1/a) - x²/a³, where a > 0, has the property that for x ≥ 0, the x-intercept is (a, 0) and the y-intercept is (0, 1/a). Let A(a) be the area of the region in the first quadrant bounded by the parabola and the x-axis. Find A(a) and determine whether it is an increasing, decreasing, or constant function of a.