The aim of the study is to assess the advancement potential of fast-growing companies, to create prerequisites for predicting the gain of such companies. The objective is to identify and forecast the growth points of the country’s economy, which is generally based on the advancement of individual economic entities, namely organizations. The research method for forecasting revenue as the main indicator of fast-growing companies (FGC) is considered. As an approximation, a logistic curve (the Ferhulst curve) is examined, the parameters of which are identified by the least squares method. Open data from financial statements of organizations are applied as a source. This work uses the criterion for distinguishing fast-growing companies; the average annual growth is of at least 50% at current prices. The novelty of the work lies in studying fast-growing organizations using a logistic curve (sigmoid). Approximation parameters are identified. A growth assessment (forecast) for organizations for 2040 is made. The statistical reliability of the selected approximation is established for 714 large and medium-sized fast-growing companies from the sample. The research results state, that a sample of about 900 fast-growing Russian companies is identified using the methods for processing large data sets from 2.5 million organizations. The illustrative calculations are based on actual sample data, highlighting the example of Wildberries in more detail. An assessment of the growth opportunities of the organizations under consideration is made. Studying the applicability of the proposed method using statistical criteria is carried out. The findings show that studying fast-growing organizations’ advancement for a medium or longer period using a logistic curve looks more preferable than applying an exponential one. For the vast majority of such organizations, the approximation of the logistic curve is statistically significant.