For the past 40 years, there has been apprehension in North American society, and particularly in the scientific community, concerning the decline of interest and enrollment in science degree programs at the post-secondary level. This trend has proven very difficult to reverse. The purpose of this study was to explore why students at an Atlantic Canadian university pursue a major in physics, and why other eligible students make different choices. Both the students themselves and their physics professors were consulted in the course of this investigation. With a post structural, constructivist theoretical framework, an instrumental case study of this university is presented using a qualitative online survey for students and semi-structured interviews with their professors. Data from this study supports the theory of physics identity proposed by Hazari et al. (2010). The themes reflected the four dimensions of physics identity, namely, interest, recognition, performance, and competence, with interest appearing as the most important of the four. One additional dimension, the "career prospects problem," was reflected within the themes of this study. This research begins to address the concern of low enrollments by examining the decision-making process of first-year physics students to stay-the-course or to pursue other options with a clear indication that as physics educationalists, we need to clearly articulate viable career options available to those who hold an undergraduate physics degree. Else, students will choose degrees whose career paths have been clearly labeled by society.