Modeling Real-World Data

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Presentation transcript:

Modeling Real-World Data Essential Questions How do we apply functions to problem situations? How do we use mathematical models to make predictions? Holt McDougal Algebra 2 Holt Algebra 2

Much of the data that you encounter in the real world may form a pattern. Many times the pattern of the data can be modeled by one of the functions you have studied. You can then use the functions to analyze trends and make predictions. Recall some of the parent functions that you have studied so far.

Because the square-root function is the inverse of the quadratic function, the constant differences for x- and y-values are switched. Helpful Hint

Identifying Models by Using Constant Differences or Ratios Use constant differences or ratios to determine which parent function would best model the given data set. The x-values increase by a constant 5. Find the differences of the y-values. 1. Time (yr) 5 10 15 20 25 Height (in.) 58 93 128 163 198 First differences: 35 35 35 35 The first differences are constant. A linear polynomial best describes the data.

Identifying Models by Using Constant Differences or Ratios Use constant differences or ratios to determine which parent function would best model the given data set. The x-values increase by a constant 4. Find the differences of the y-values. 2. Time (yr) 4 8 12 16 20 Population 10,000 9,600 9,216 8,847 8,493 First differences: -400 -384 -369 -354 Second differences: 16 15 15 Ratio: The ratios are constant. An exponential function best describes the data.

Identifying Models by Using Constant Differences or Ratios Use constant differences or ratios to determine which parent function would best model the given data set. The x-values increase by a constant 1. Find the differences of the y-values. 3. Time (s) 1 2 3 4 5 Height (m) 132 165 154 99 First differences: 33 -11 -55 -99 Second differences: -44 -44 -44 The second differences are constant. A quadratic polynomial best describes the data.

Identifying Models by Using Constant Differences or Ratios Use constant differences or ratios to determine which parent function would best model the given data set. The y-values increase by a constant 10. Find the differences of the x-values. 4. x 12 48 108 192 300 y 10 20 30 40 50 First differences: 36 60 84 108 Second differences: 24 24 24 The second x-value differences are constant. A square root function best describes the data.

Identifying Models by Using Constant Differences or Ratios Use constant differences or ratios to determine which parent function would best model the given data set. The x-values increase by a constant 1. Find the differences of the y-values. 5. x 21 22 23 24 y 243 324 432 576 First differences: 81 108 144 Second differences: 27 36 Ratio: The ratios are constant. An exponential function best describes the data.

Lesson 15.3 Practice A