At the end of this lesson, students will be able to:
- Identify functions using differences and ratios.
- Write equations for functions.
- Perform exponential and quadratic regressions with a graphing calculator.
- Solve real-world problems by comparing function model.
Terms introduced in this lesson:
ratio of the differences
constant ratio of differences
exponential, quadratic regression
Teaching Strategies and Tips
Emphasize that students should always begin a regression by drawing the scatter plot of the data. This allows them to determine which function of best fit is most appropriate, if any.
- A regression is a curve that comes as close as possible to all the data points without being another type of function.
- Regressions do not necessarily pass through data points. Therefore, values will be different from those in the data set.
Remind students to check in general the differences in values that they are constant.
In Review Questions 4-6 and 12, remind students to calculate the differences of the differences to see if a quadratic trend exists. Students often calculate only the first set of differences.