9.2.3 Modeling Real-World Data Key Objectives • Apply functions to problem situations. • Use mathematical models to make predictions.
Real-world data that forms a pattern can often be modeled by a function, such as a linear, quadratic, polynomial, exponential, or square-root function. That function can be used to analyze trends in the data and make predictions about the data. Example 1 Identifying Models by Using Constant Differences or Ratios The differences between or ratios of consecutive values in a data set can often be used to determine which parent function would best model the data. • Linear Function: Constant first differences between y -values for evenly spaced x -values. • Quadratic Function: Constant second differences between y -values for evenly spaced x -values. • Exponential Function: Constant ratios between y -values for evenly spaced x -values. • Square Root Function: Constant second differences between x -values for evenly spaced y -values
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