In this lesson, students use the main function types they have studied thus far in the course (linear and exponential) to model different populations.

For timing, it may be appropriate to select only one of the modeling tasks. The first task focuses on selecting an appropriate model (linear, exponential, or neither) for given data, then writing a function for the model. The second task focuses on researching additional data, examining data on different time intervals, and breaking a single set of data into pieces that can be modeled differently on different time intervals. Select the task that would better support students’ understanding.

Students engage in different parts of the modeling cycle (MP4). This can be adjusted further, for example, by choosing other cities for the first activity and having students find the data. They will have to think carefully (MP1) about how to choose an appropriate linear or exponential model because none of the data is exactly exponential or linear. They will also attend to precision (MP6) in choosing the parameters in their models.