Transfer learning (TL) is a powerful machine learning tool, particularly deep learning, enabling models to adapt to new tasks by leveraging prior knowledge. However, continual learning poses challenges, especially with domain adaptation. This work addresses these challenges by initially training a model from scratch on the CIFAR-100 dataset (source task), then transferring its knowledge to an intermediate task involving a Kaggle cancer dataset, followed by an additional transfer to a lung infection dataset (target task). While the models perform strongly on the intermediate task, they struggle on the target task due to continual learning challenges. To overcome this, the paper proposes using Elastic Weight Consolidation (EWC) to significantly improve test accuracy on the target task across various architectures, highlighting the importance of domain adaptation techniques in continual learning. Specifically, InceptionV3 demonstrates superior performance with notably improved metrics, achieving a test loss reduction of 0.82. EWC proves particularly effective when models are trained from scratch, as it helps to preserve important features by penalizing changes to critical weights. However, its effectiveness diminishes when applied to pre-trained models, such as those initialized with ImageNet weights, due to the optimized nature of these weights for general image recognition tasks. Thus, EWC is shown to be beneficial in scenarios involving models trained from scratch.