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CCGPS CA 4.2.2 Example 2: Modeling Student Enrollment with Exponential Functions

CCGPS CA 4.2.2 Example 2: Modeling Student Enrollment with Exponential Functions
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2012-05-30 23:56
FunctionSequenceOptimizationSlider AnimationGraphing
In collections CCGPS CA Unit 4 Lesson 2
Example 2 of CCGPS CA 4.2.2 illustrates how to use GeoGebra to create a scatter plot of eight years of student enrollment data and fit an exponential function to model the growth trend. The construction employs Corner, Textfield, Sequence, Segment, Polygon, and VerticalText commands, generating objects such as A1–B9 and a Slid slider for parameter adjustment. Core concepts include exponential functions, regression analysis, scatter plots, means, distributions, and linear programming optimization. This resource is ideal for high‑school students studying exponential modeling and for introductory college statistics or mathematical modeling courses.

GeoGebra Commands & Parameters

  1. Corner(2) → Corn2
  2. Corner(3) → Corn3
  3. Textfield(A2) → InA2
  4. Textfield(A3) → InA3
  5. Textfield(A4) → InA4
  6. Textfield(A5) → InA5
  7. Textfield(A6) → InA6
  8. Textfield(A7) → InA7
  9. Textfield(A8) → InA8
  10. Textfield(A9) → InA9
  11. Textfield(B9) → InB9
  12. Textfield(B8) → InB8
  13. Textfield(B7) → InB7
  14. Textfield(B6) → InB6
  15. Textfield(B5) → InB5
  16. Textfield(B4) → InB4
  17. Textfield(B3) → InB3
  18. Textfield(B2) → InB2
  19. Sequence(Segment[(10.5, 100 + (80 * j)), (14, 100 + (80 * j))], j, 0, 8) → LnList
  20. Sequence(Segment[(14, 100 + (80 * j)), (16, 100 + (80 * j))], j, 0, 8) → LnList3
  21. Sequence(Segment[(10.5 + (1.75 * j), 100), (10.5 + (1.75 * j), 860)], j, 0, 2) → LnList2
  22. Segment((10.5, 860), (14, 860)) → Top1
  23. Segment((14, 860), (16, 860)) → Top2
  24. Segment((16, 100), (16, 860)) → Side1
  25. Polygon((0.5 * Corner[1]) + (0.5 * Corner[2]), Corner[2], Corner[3], (0.5 * Corner[3]) + (0.5 * Corner[4])) → poly1, b, c, d, e
  26. VerticalText("Students") → Students

AI Drawing Prompt Reference

Create a scatter plot of eight years of student enrollment data with an exponential fit. Draw a grid: horizontal lines from y=100 to 860 every 80 units, vertical lines from x=10.5 to 14 every 1.75 units, plus top and right border segments; fill the background with a rectangle covering half the view. Place a vertical “Students” label on the left. Provide eight editable text boxes for the years (A2‑A9) and enrollment numbers (B2‑B9), and add a slider to adjust the exponential model parameters so the fitted curve updates interactively.
The prompt above was compiled from the original drawing commands and is for reference only.