The universe is currently expanding and accelerating, with dark energy driving this acceleration. A well-known model, ΛCDM, assumes dark energy is a cosmological constant, but alternative models like quintessence, which involve a scalar field, are also considered. This paper explores an exponential quintessence model with potential $ V = V_0 e^{-\lambda \phi} $, focusing on its cosmological implications and compatibility with string theory. The model is analyzed in a 4-dimensional dynamical system framework, considering radiation, matter, and spatial curvature. The study reveals that for $ \lambda \geq \sqrt{2} $, the model can lead to transient acceleration, while for $ \lambda \leq \sqrt{2} $, it allows for a stable accelerating universe. The analysis includes a detailed examination of fixed points, their stability, and the behavior of cosmological solutions. The results show that the model can reproduce the observed universe's evolution, with constraints on $ \lambda $ derived from observational data. The paper also discusses the potential for string theory realizations of the model and its implications for the nature of dark energy and fundamental constants. The findings suggest that exponential quintessence models with $ \lambda \geq \sqrt{2} $ could be viable for describing dark energy in our universe, particularly when spatial curvature is included. The study provides theoretical predictions for model parameters and highlights the importance of considering both observational and theoretical constraints in understanding the universe's accelerated expansion.The universe is currently expanding and accelerating, with dark energy driving this acceleration. A well-known model, ΛCDM, assumes dark energy is a cosmological constant, but alternative models like quintessence, which involve a scalar field, are also considered. This paper explores an exponential quintessence model with potential $ V = V_0 e^{-\lambda \phi} $, focusing on its cosmological implications and compatibility with string theory. The model is analyzed in a 4-dimensional dynamical system framework, considering radiation, matter, and spatial curvature. The study reveals that for $ \lambda \geq \sqrt{2} $, the model can lead to transient acceleration, while for $ \lambda \leq \sqrt{2} $, it allows for a stable accelerating universe. The analysis includes a detailed examination of fixed points, their stability, and the behavior of cosmological solutions. The results show that the model can reproduce the observed universe's evolution, with constraints on $ \lambda $ derived from observational data. The paper also discusses the potential for string theory realizations of the model and its implications for the nature of dark energy and fundamental constants. The findings suggest that exponential quintessence models with $ \lambda \geq \sqrt{2} $ could be viable for describing dark energy in our universe, particularly when spatial curvature is included. The study provides theoretical predictions for model parameters and highlights the importance of considering both observational and theoretical constraints in understanding the universe's accelerated expansion.