The surface density profile Σ(r) of the solar nebula protoplanetary disk is a fundamental input to all models of disk processes and evolution. Traditionally it is estimated by spreading out the augmented masses of the planets over the annuli in which the planets orbit today, the so-called minimum-mass solar nebula. Doing so implicitly assumes that the planets completely accreted all planetesimals in their feeding zones, but this assumption has not been tested. Indeed, models of the growth of Uranus and Neptune predict that these planets could not have grown to ~10 M⊕ within the lifetime of the disk, even though they must have, to accrete H/He atmospheres. In this paper we adopt the starting positions of the planets in the ``Nice'' model of planetary dynamics (Tsiganis and coworkers), in which the solar system started in a much more compact configuration. We derive a surface density profile that is well approximated by the power law Σ(r)=343(fp/0.5)-1(r/10 AU)-2.168 g cm-2, where fp is the fraction of the solid mass in the form of planetesimals. We show that this profile is inconsistent with a steady state accretion disk but is consistent with a steady state decretion disk that is being photoevaporated. We calculate the growth of planets in the context of this disk model and demonstrate for the first time that all of the giant planets can achieve their isolation masses and begin to accrete H/He atmospheres within the lifetime of the disk. The fit of our inferred Σ(r) to the augmented masses of the planets is excellent (<10%), but only if Uranus and Neptune swtiched places early in the solar system's evolution, a possibility predicted by the Nice model.