In the present study, an innovative analytical technique for solving nonlinear biodegradation equations of n-butanol in biofilters is introduced, which uses Taylor's method. The purpose is to produce results that are accurate and efficient. Finally, the main purpose in creating this model is to predict the n-butanol concentration level in both phases such as biofilm and gas, which is important to optimize the biofiltration processes. The methodology used encompasses the application of Taylor series expansion in approximating the solutions of these complex nonlinear equations, which provide a means of an iterative solution that leads to a closed form. This method is indeed very important because it is reducing the complexity in terms of computation while providing the necessary reliable predictions, thereby making it very essential in designing and scaling biofilters. Results from this approach were found to be in very great correlation with existing numerical methods, thus validating correctness of the approach. This discussion shows the superiority of Taylor's method for nonlinear biodegradation processes, but it also opens avenues into adapting this for other types of volatile organic compounds and for various biofilter configurations. The work sets the way forward for further research to be done on biofiltration methods for volatile pollutants.