A semi-analytical expression has been developed that accurately models the population dynamics of an aerosol growing from the detection limit (3 nm) to a characteristic CCN size (100 nm), quantifying the contributions of size and time-dependent source and sink terms such as coagulation of smaller particles and scavenging by the pre-existing aerosol. These model inputs were calculated from measured aerosol size distributions and growth rates acquired during intensive measurement campaigns in Boulder, CO, Atlanta, GA, and Tecamac, Mexico. Twenty CCN formation events from these campaigns were used to test the validity of this model. Measured growth rates ranged from 3-22 nm/h. The modeled and measured CCN production probabilities agreed well with each other, ranging from 1-20%. The pre-existing CCN number concentration increased on average by a factor of 3.8 as a result of new particle formation.