In this lesson, students use the main function types they have studied thus far in the course (linear and exponential) to model different populations. In the first activity, data for three city populations are given and students are asked to produce a linear or exponential model for each (if appropriate) and then make predictions for populations at other dates. The cities have been chosen so that one is well modeled by an exponential model, another by a linear model, and the third by neither.
In the second activity, students examine world population. The task is more open-ended and only limited data is provided, likely requiring students to gather more data. In addition, the world population is not consistently well modeled by a linear or exponential function, but for certain periods of time, exponential and/or linear functions can be appropriate (in particular, in recent years the growth has been strikingly linear).
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.
- Choose and write a linear or exponential function to model real-world data.
- Determine and explain (in writing) how well a function models the given data.
- Use given population data to calculate or estimate growth rates and make predictions.
Let's use linear and exponential models to represent and understand population changes.
If students are to present their mathematical models on visual displays, prepare tools for creating visual displays.
Acquire devices that can run Desmos (recommended) or other graphing technology. It is ideal if each student has their own device. (Desmos is available under Math Tools.)
- I can determine how well a chosen model fits the given information.
- I can determine whether to use a linear function or an exponential function to model real-world data.