In this article, we adapt the estimator based on the exponential function for the estimation of the population mean in the presence of non-response on both the study and the auxiliary variables. The expressions for the Bias and Mean Square Error (MSE) are derived to the first degree of approximation and theoretical comparisons are made with existing estimators in literature. We demonstrate that the adapted estimator is more efficient than compared estimators, such as classical ratio and regression estimators, Hansen-Hurwitz unbiased estimator, and the estimator of Singh et al. (2009) under the obtained conditions. Furthermore, these theoretical results are supported numerically by providing an empirical study on seven different data sets presenting the efficiency of the adapted estimator.