The primary emphasis of this paper is to study about two nonlinear growth models, the Janoschek growth model, and Sloboda growth model. The key aim is to introduce new methods of estimation for estimating the parameters in the Janoschek growth model and the Sloboda growth model. Examining this paper also offers more effective approaches to address the properties inherent in the models. While conventional nonlinear optimization techniques typically demand extensive computational efforts for the estimation of parameters. In contrast, the methods introduced herein, offer simplicity of understanding, making them suitable for smaller datasets, and enhancing their relevance across diverse contexts.