Algebra 1 / Unit 9: Quadratic Functions and Equations
9.7 Comparing Linear, Quadratic and Exponential Models
Notes
Pick the model that fits how the data change over equal steps in $x$:
- Linear: constant first differences (adds the same amount).
- Quadratic: constant second differences.
- Exponential: constant ratio (multiplies by the same factor).
- An increasing exponential function eventually grows faster than any linear or quadratic function.
Practice
Outputs at $x = 0, 1, 2, 3$: 5, 8, 13, 20. Which model fits?
First differences 3, 5, 7; second differences constant at 2.
Outputs at $x = 0, 1, 2, 3$: 4, 12, 36, 108. Which model fits?
Each output is 3 times the last.
Which will be greatest for large values of $x$?
Exponential growth eventually beats polynomial growth.
Ready for more? Take the Unit 9 test.