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10.7: Linear, Exponential and Quadratic Models

Created by: CK-12

Learning Objectives

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.

Vocabulary

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.

Point out:

  • 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, y-values will be different from those in the data set.

Remind students to check in general the differences in x-values that they are constant.

Error Troubleshooting

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.

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CK.MAT.ENG.TE.1.Algebra-I.10.7

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