In this study, the ${AA}$ngstrom exponent for polydispersed aerosol during dynamic processes was investigated. Log-normal aerosol size distribution was assumed, and a sensitivity analysis of the ${AA}$ngstrom exponent with regards the coagulation and condensation process was performed. The ${AA}$ngstrom exponent is expected to decrease because of the particle growth due to coagulation and condensation. However, it is difficult to quantify the degree of change. In order to understand quantitatively the change in the ${AA}$ngstrom exponent during coagulation and condensation, different real and imaginary parts of the refractive index were considered. The results show that the ${AA}$ngstrom exponent is sensitive to changes in size distribution and refractive index. The total number concentration decreases and the geometric mean diameter of aerosols increase during coagulation. On the while, the geometric standard deviation approaches monodispersed size distribution during the condensation process, and this change in size distribution affects the ${AA}$ngstrom exponent. The degree of change in the ${AA}$ngstrom exponent depends on the refractive index and initial size distribution, and the size parameter changes with the ${AA}$ngstrom exponent for a given refractive index or chemical composition; this indicates that the size distribution plays an important role in determining the ${AA}$ngstrom exponent as well as the chemical composition. Subsequently, this study shows how the ${AA}$ngstrom exponent changes quantitatively during the aerosol dynamics processes for a log-normal aerosol size distribution for different refractive indices; the results showed good agreement with the results for simple analytic size distribution solutions.