Interstellar dust containing carbon will necessarily have optical cons
tants that respond to the local environment of the dust. This response
may be sufficiently slow that the extinction produced by such dust ma
y change on time-scales that are comparable to the likely cloud age. T
herefore, interstellar extinction caused by carbon-containing dust sho
uld evolve in time. We explore this concept through a model of dust in
which H-rich amorphous carbon is deposited on silicate substrates in
the interstellar medium, and is annealed to form H-poor amorphous carb
on. We find that, in this model, the interstellar extinction is sensit
ive to the gas density (which controls the rate of carbon depletion) a
nd to the UV radiation field (which controls the annealing rate). In c
louds typical of the diffuse interstellar medium, the initial extincti
on curve is fairly flat in the far UV, becomes similar to the 'standar
d' interstellar curve after about 1-2 Myr, and remains similar to the
standard curve for about a further 1 Myr. The curve then steepens in t
he far UV. The wide variations in the observed extinction may therefor
e simply reflect time-evolution of the dust properties.