Examples of the predicted ¹³CO R(4) and C¹⁸O R(6) emission for a continuous power-law distribution of temperature and column density that describe the ¹²CO P(9) line-profile and the ¹²CO rotational diagram. Colors in the spectra and rotational diagrams correspond to the different column density distributions in the first panel. A disk model with a single power-law surface density cannot simultaneously reproduce the ¹²CO, ¹³CO, and C¹⁸O line-profiles and rotational diagrams.