We present a theoretical framework combining exponential growth dynamics and Michaelis-Menten kinetics to model the interaction between tumor density and drug concentration delivered via an infusion pump. The model accounts for the saturation of tumor growth inhibition at high drug concentrations, reflecting biological saturation effects. Continuous infusion chemotherapy is highlighted as a superior delivery method, maintaining consistent drug levels at the tumor site while reducing systemic side effects compared to conventional bolus methods. The framework provides a predictive tool for determining the critical drug concentrations and tumor densities required for tumor elimination while minimizing adverse effects. Stability analysis, based on solving nonlinear equations, identifies equilibrium points that represent steady states of tumor density and drug concentration. The stability of these points is examined to assess the long-term effectiveness of chemotherapy regimens. Illustrative numerical simulations demonstrate how variations in drug delivery rates, tumor properties, and kinetic parameters influence therapeutic outcomes. Key factors such as the minimum drug concentration needed to suppress tumor growth and conditions for tumor eradication or regrowth are identified. Sensitivity analysis further reveals how parameter changes affect system stability and outcomes, offering insights for optimizing dosing strategies. This framework bridges theoretical modeling and practical challenges in cancer chemotherapy, providing a versatile tool for understanding and improving treatment strategies. It can be adapted to various tumor types and treatment modalities, supporting advancements in personalized medicine and future cancer therapy research.