Cellular growth impacts a range of phenotypic responses. Identifying the sources of fluctuations in growth and how they propagate across the cellular machinery can unravel mechanisms that underpin cell decisions. In this talk, I will present a stochastic cell model linking gene expression, metabolism and replication to predict growth dynamics in single bacterial cells. In addition to several population-averaged data, the model quantitatively recovers how growth fluctuations in single cells change across nutrient conditions. We also developed a theoretical framework to analyse stochastic chemical reactions coupled with cell divisions, and used it to identify sources of growth heterogeneity. By visualising cross-correlations we then determined how initial fluctuations propagate to growth rate and affect other cell processes. Finally, we study antibiotic responses and find that complex drug-nutrient interactions can both enhance and suppress heterogeneity. Our results provide a predictive framework to integrate single-cell and bulk data and draw testable predictions with implications for antibiotic tolerance, evolutionary biology and synthetic biology.