An alternative to conventional antibiotics is needed to fight against emerging multiple drug resistant pathogenic bacteria. In this endeavor, the effect of silver nanoparticle (Ag-NP) has been studied quantitatively on two common pathogenic bacteria Escherichia coli and Staphylococcus aureus, and the growth curves were modeled. The effect of Ag-NP on bacterial growth kinetics was studied by measuring the optical density, and was fitted by non-linear regression using the Logistic and modified Gompertz models. Scanning Electron Microscopy and fluorescence microscopy were used to study the morphological changes of the bacterial cells. Generation of reactive oxygen species for Ag-NP treated cells were measured by fluorescence emission spectra. The modified Gompertz model, incorporating cell death, fits the observed data better than the Logistic model. With increasing concentration of Ag-NP, the growth kinetics of both bacteria shows a decline in growth rate with simultaneous enhancement of death rate constants. The duration of the lag phase was found to increase with Ag-NP concentration. SEM showed morphological changes, while fluorescence microscopy using DAPI showed compaction of DNA for Ag-NP-treated bacterial cells. E. coli was found to be more susceptible to Ag-NP as compared to S. aureus. The modified Gompertz model, using a death term, was found to be useful in explaining the non-monotonic nature of the growth curve. The modified Gompertz model derived here is of general nature and can be used to study any microbial growth kinetics under the influence of antimicrobial agents.