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Early detection of dementia is critical for effective symptom management. Recent studies have aimed to develop machine learning (ML) models to identify dementia onset and severity using language and speech features. However, existing methods can lead to serious privacy concerns due to sensitive data collected from a vulnerable population. In this work, we aim to establish the privacy-accuracy tradeoff benchmark for dementia classification models using audio and speech features. Specifically, we explore the effects of differential privacy (DP) on the training phase of the audio model. We then compare the classification accuracy of DP and non-DP models using a publicly available dataset. The resultant comparison provides useful insights to make informed decisions about the need for balancing privacy and accuracy tradeoff for dementia classification tasks. Our findings have implications for real-world deployment of ML models to support early detection and effective management of dementia.