We formulate and calculate the evolution of dust in a galaxy focusing on the distinction among various dust components – silicate , aromatic carbon , and non-aromatic carbon . We treat the galaxy as a one-zone object and adopt the evolution model of grain size distribution developed in our previous work . We further include aromatization and aliphatization ( inverse reaction of aromatization ) . We regard small aromatic grains in a radius range of 3–50 Å as polycyclic aromatic hydrocarbons ( PAHs ) . We also calculate extinction curves in a consistent manner with the abundances of silicate and aromatic and non-aromatic carbonaceous dust . Our model nicely explains the PAH abundance as a function of metallicity in nearby galaxies . The extinction curve become similar to the Milky Way curve at age \sim 10 Gyr , in terms of the carbon bump strength and the far-ultraviolet slope . We also apply our model to starburst galaxies by shortening the star formation time-scale ( 0.5 Gyr ) and increasing the dense-gas fraction ( 0.9 ) , finding that the extinction curve maintains bumpless shapes ( because of low aromatic fractions ) , which are similar to the extinction curves observed in the Small Magellanic Cloud and high-redshift quasars . Thus , our model successfully explains the variety in extinction curve shapes at low and high redshifts .