Lead-acid (PbA) batteries are a key component in contemporary conventional and hybrid electric vehicles (HEV), as they play the key role of providing starting-lightning-ignition (SLI) functionality in the vehicle. In this paper, a semi-empirical model of a 12 V SLI PbA battery is developed that incorporates major electrochemical phenomena of the battery, including major degradation mechanisms that are relevant to SLI PbA batteries. The purpose of the model is to establish the feasibility of extracting features of the battery state of health (SOH) from its step response. An aging campaign based on a modified version of the IEC 60095-1 standard is used to age a battery, and the resulting data is used to validate the model. By estimating the exchange current and charge transfer resistances of the electrodes at regular intervals, it is shown that they exhibit a monotonic correlation with battery capacity degradation. The model is further validated with data from a battery aged under real-world conditions. The novelty of this work lies in the demonstration that the effect of the dominant aging mechanisms on battery capacity can be extracted using data obtained from a short step response (roughly 7 seconds), paving the way for real-time SOH estimation algorithms.