This is the first of several lessons in which students practice modeling situations by using sequences and then use their models to understand different aspects of the situation, translating between the situations and their representations (MP2). This isn’t meant to be the full modeling cycle, but rather a focus on some practices that students must attend to while modeling (MP4). In this lesson, students describe a reasonable domain for a function representing a context in which an unrestricted domain does not make sense. They also encounter a situation in which a recursive model is straightforward to write, while one for the term is not, leading to the ideas that sometimes the model we use depends on what we are trying to do and that some representations are more efficient than others to achieve our goals.

Encourage students to represent the sequences in multiple ways to help them make sense of the patterns. These lessons also provide opportunity for students to recall and use techniques they may have learned in earlier courses about modeling linear and exponential functions. It is also important to note that the work students do modeling situations with geometric sequences here will be built upon in a future unit on exponential functions.