There are a couple of purposes in this paper: to study a problem of approximation with exponential functions and to show its relevance for the economic science. We present results that completely solve the problem of the best approximation by means of exponential functions and we will be able to determine what kind of data is suitable to be fitted. Data will be approximated using TAC (implemented in the R-package nlstac), a numerical algorithm for fitting data by exponential patterns without initial guess designed by the authors. We check one more time the robustness of this algorithm by successfully applying it to two very distant areas of economy: demand curves and nonlinear time series. This shows TAC's utility and highlights how far this algorithm could be used.

翻译：本文旨在研究通过指数函数进行逼近的问题，并展示其在经济科学中的相关性。我们提出的结果完全解决了指数函数最佳逼近问题，并能够确定何种类型的数据适合进行拟合。数据将采用TAC（已实现于R包nlstac中）进行逼近，该数值算法由作者设计，无需初始猜测即可通过指数模式拟合数据。我们通过将该算法成功应用于两个相距甚远的经济领域——需求曲线与非线性时间序列，再次验证了其鲁棒性。这证明了TAC的实用性，并凸显了该算法的广泛应用潜力。