Individual cells grown in culture exhibit remarkable differences in their growth, with some cells capable of forming large clusters, while others are limited or fail to grow at all. While these differences have been observed across cell lines and human samples, the growth dynamics and associated cell states remain poorly understood. In this study, we performed clonal tracing through imaging and cellular barcoding of an in vitro model of esophageal epithelial cells (EPC2-hTERT). We found that about 10% of clones grow exponentially, while the remaining have cells that become non-proliferative leading to a halt in the growth rate. Using mathematical models, we demonstrate two distinct growth behaviors: exponential and logistic. Further, we discovered that the propensity to grow exponentially is largely heritable through four doublings and that the less proliferative clones can become highly proliferative through increasing plating density. Combining barcoding with single-cell RNA-sequencing (scRNA-seq), we identified the cellular states associated with the highly proliferative clones, which include genes in the WNT and PI3K pathways. Finally, we identified an enrichment of cells resembling the highly proliferative cell state in the proliferating healthy human esophageal epithelium.