High School Frog Population Tracking GeoGebra Example

GeoGebra Commands & Parameters

1. Length(frogs) → numpts
2. LaTeX(steps) → counter
3. LaTeX("\text{Move the slider to solve the problem.}") → text0
4. Corner(1) → A
5. Corner(3) → B
6. TableText({{"frogs,n", Element[frogs, 1], Element[frogs, 2], Element[frogs, 3], Element[frogs, 4], Element[frogs, 5], Element[frogs, 6], Element[frogs, 7], Element[frogs, 8], Element[frogs, 9]}, {"weeks,t", 1, 2, 3, 4, 5, 6, 7, 8, 9}}, "c") → table
7. LaTeX(table) → Problem
8. LaTeX("\text{Create a scatter plot of the table values.}") → text1
9. Sequence((i, Element[frogs, i]), i, 1, numpts) → plot
10. Fit(plot, (a * b^(x))) → f
11. Fit(plot, (c * x^(d))) → g
12. LaTeX(g, true, true) → text6
13. LaTeX("\text{Which function fits the data best?}") → text7
14. Sequence((Element[frogs, i] - f(i))^(2), i, 1, numpts) → fdiffs
15. Sequence((Element[frogs, i] - g(i))^(2), i, 1, Length[frogs]) → gdiffs
16. Sum(fdiffs) → fms
17. Sum(gdiffs) → gms
18. LaTeX("\text{Fit an exponential function of the form }\textcolor{#006633}{f(x) = a b^x}\text{ to the data.}") → text3
19. LaTeX("\text{Fit a power function of the form }\textcolor{#CC0000}{g(x) = c x^d}\text{ to the data.}") → text5
20. LaTeX("\text{Does the shape of the function look similar to the shape of the data}\cr\text{or does the function appear to be headed off in a different direction}\cr\text{from the data?}") → text8
21. LaTeX("\text{Is one function consistently closer to the individual data points than the other?}") → text10
22. LaTeX("\text{Do the functions do anything obviously unreasonable if they are used }\cr\text{to predict values {outside the range of collected data?}") → text12
23. LaTeX("\text{Neither function does this. We know in general that exponential }\cr\text{growth cannot occur indefinitely, but that it does occur temporarily.}") → text13
24. LaTeX("\text{Use the buttons below to return to the original problem or}\cr\text{randomly generate a similar practice problem.}") → RandomizationText
25. If(angleMargin < (-0.2), LaTeX["\text{The }\textcolor{#006633}{exponential} \text{ function does better with this.}"], If[angleMargin > 0.2, LaTeX["\text{The }\textcolor{#CC0000}{power}\text{ function does better with this.}"], LaTeX["\text{The functions are similar in this respect.}"]]) → text9
26. If(margin < (-0.2), LaTeX["\text{The }\textcolor{#006633}{exponential}\text{ function does better with this.}"], If[margin > 0.2, LaTeX["\text{The }\textcolor{#CC0000}{power}\text{ function does better with this.}"], LaTeX["\text{The functions are similar in this respect.}"]]) → text11
27. LaTeX("\text{Data points should not be connected by any lines.}") → text2
28. LaTeX((("\textcolor{#006633}{f(x)=" * f) * "} \text{ Note: functions may vary.}")) → text4
29. Length(frogs_1) → numpts_1
30. Sequence((i, Element[frogs_1, i]), i, 1, numpts_1) → plot_1
31. Fit(plot_1, (a * b^(x))) → f_1
32. LaTeX("\text{ Note: functions may vary.}") → text4_1