###### Abstract  
This paper explores the application of a mathematical trend model to analyze product sales performance. A logistic trend model was utilized to analyze product sales performance, employing monthly sales data collected over three years. The model assessed impacts across various phases of the product life cycle. Significant sales trends were identified and modeled from historical data, demonstrating how sales dynamics mirror broader economic phenomena and consumer behaviors. In addition to logistic trends, linear and quadratic trends were also evaluated. To assess the significance of the sales trends for three products, the Mann-Kendall test was applied. The results indicate a statistically significant positive trend in the sales of product A. For evaluating the quality of data fit in model comparison, the Akaike Information Criterion (AIC) and the Bayesian Information Criterion (BIC) were deemed appropriate. The analysis revealed that the logistic model effectively delineates different sales phases--from introduction to maturity--and highlights opportunities for optimizing strategic sales planning and customer satisfaction in alignment with market demands. The study's findings are crucial for businesses seeking to enhance product lifecycle management and boost sales forecasting precision. G 2025 15 4695 13 March 2025 19 April 2025 21 April 2025 21 April 2025 21 April 2025 21 May 2025 2  
growth and saturation trends, provides essential insights that help businesses stay resilient and proactive in a rapidly changing economic environment. The Gompertz model is a widely used framework for describing growth phenomena characterized by an initial period of exponential growth that gradually slows as it approaches a maximum saturation level. This model is distinctive for its asymmetric, sigmoidal shape, which captures the often observed slowing of growth as a population approaches its carrying capacity or other limiting factors [1]. First introduced by [PERSON] in 1825, the model has since been applied across a variety of disciplines, from biological processes to technological advancements and market trends [2]. The [PERSON] model is vital for aligning sales strategies with market demands, forecasting demand for new products, and managing life cycles of existing ones. By predicting stages of product adoption and saturation, it helps businesses optimize strategies for maximum impact. Implementations such as quality support, rapid problem resolution, and personalized services like targeted recommendations and customizable options, enhance customer satisfaction and loyalty. Informed by the [PERSON] model, these strategies exceed customer expectations, boosting brand loyalty and market share. One of the key advantages of the [PERSON] model is its flexibility in modeling complex growth dynamics with relatively few parameters. As [3] explains, the model \"provides robust long-term predictions,\" even when only limited early-stage data are available. This makes it particularly useful in forecasting trends in various industries, where early data points may be scarce, but reliable projections are necessary for decision-making. The model's ability to predict future growth based on historical data are further enhanced by its capacity to adjust as more data accumulates [4]. Another significant advantage is the model's performance in comparison to simpler symmetric models. While models like the logistic model assume symmetric growth, the Gompertz model's asymmetric nature allows it to better represent real-world dynamics, particularly those with slower rates of growth as the system matures [1]. Furthermore, recent studies have proposed generalizations of the Gompertz model, incorporating additional parameters to capture a more diverse range of growth behaviors, increasing its overall applicability and accuracy [5]. In the face of rapid advancements and the unpredictability of modern markets, the introduction of predictive models like the Gompertz curve has become imperative.