A Comparative Analysis of Exponential and Reciprocal Mathematical Models to Describe the Cooling Process of a Cup of Tea

This investigation explores whether an exponential or reciprocal mathematical model best describes the cooling process of a cup of tea. The author collected primary temperature data over 6,840 seconds, developing both an exponential decay function and a reciprocal function to fit the observations.

Using linearization techniques and Pearson’s correlation coefficients, the author compared the models' accuracy. Although both showed strong correlations, the exponential model was chosen for its superior alignment with the ambient room temperature asymptote. The final model was applied to determine the optimal drinking window between 60°C and 30°C. This exemplar is valuable for its comparative modeling approach and the use of data transformation to validate non-linear relationships.