Bacterial persistence is a phenomenon where a subpopulation of cells can survive antibiotic treatment, and it is often linked to extremely slow growth or a dormant state. However, the mechanisms and factors that govern dormancy are not well understood. We propose a simplified growth model that treats the main cellular components as discrete variables and allocates resources among them according to different strategies. The model can reproduce some of the observed features of bacterial persistence, such as wide distribution in division times, long division times after a nutrient downshift, and the existence of different dormant phenotypes. We also show how the growth structure, i.e., whether cells grow in a lineage or a branch, affects the dormant cells' occurrence and distribution due to the growth states' mother-daughter correlation. Our model provides a framework to explore the complex interactions between cellular processes and environmental conditions that lead to bacterial persistence.