In this article we present a reflection about the meaning attribution to the mathematical object "exponential function" that emerges from two mathematical modeling activities. The theoretical framework of the text contemplates considerations on Mathematical Modeling and elements of semiotics as theorized by Charles Sanders Peirce. The empirical research refers to the development of two modeling activities carried out by different groups of students. We analyzed the interpretant signs produced by students working in groups on two activities. The analysis indicates that exponential function meaning in mathematical modeling activities is associated with the "familiarity" that the interpreter reveals to have in relation to the object; the interpreter's "intention" in signifying the object; the identification, by the interpreter, of the possibility to refer to the object in other circumstances or in future situations; and the "collateral experience" of the interpreter with the object. In addition, the significance of the exponential function in modeling activities is also associated with the specificities of the problem as well as with the pertinent systems of practices and contexts of use of this function.