Bacteria persistence is a well-known phenomenon, where a small fraction of cells in an isogenic population are able to survive high doses of antibiotic treatment. Since the persistence is often associated with single cell behaviour, the ability to study the dynamic response of individual cells to antibiotics is critical. In this work, we developed a gradient microfluidic system that enables long-term tracking of single cell morphology under a wide range of inhibitor concentrations. From time-lapse images, we calculated bacterial growth rates based on the variations in cell mass and in cell number. Using E. coli and Comamonas denitrificans to amoxicillin inhibition as model systems, we found the IC50 determined via both methods are in a good agreement. Importantly, the growth rates together with morphological dynamics of individual cells has led to the discovery of a new form of persistence to amoxicillin. Normal cells that are sensitive to amoxicillin gain persistence or recover from the killing process, if they have had an opportunity to utilise the cytoplasm released from lysed cells close-by. We term this acquired persistence in normal growing cells "opportunistic persistence". This finding might shed new insights into biofilm resistance and the effect of antibiotics on environmental microbes.