The time-dependent properties of an Ar/C2H2 dusty plasma (neutral, ion and electron densities, effective electron temperature and dust charge) are studied using a volume-averaged model for conditions corresponding to experiments on nanoparticle growth. The calculated density evolution for C2H2, H2 and C4H2 molecules are compared with time-resolved measurement of the mass peaks of the neutral species and the effects of the dust density on the plasma properties are analyzed. Time evolutions of the main positive and negative ions are also obtained thanks to the calculations. As a consistency check the time-dependence of the dust radius is also obtained numerically, assuming that an increase of the dust radius is due to deposition of hydrocarbon ions and C2H radicals on the surface of dust particles. It is shown that for conditions corresponding to the experiment, the ions are the main contributor to the particle growth. The calculated dust growth rate is compared to the time-dependence of the dust particle size obtained in the experimental measurements. The results of the numerical calculations are found to be in a good qualitative agreement with the experimental data.