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# Growth of a Green Bean

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### Growth of a Green Bean

1. 1. Green beanprojectJason KohMHF4U
2. 2. Under direct sun (table)Days Height1 02 2.83 64 95 116 13.67 158 16.89 17.610 18.4
3. 3. Scatter plot
4. 4. Linear
6. 6. Cubic
7. 7. Quartic
8. 8. Quintic
9. 9. Exponential
10. 10. Logarithmic
11. 11. Best fit functionModel R2Linear 0.9592Quadratic 0.9982Cubic 0.9992Quartic 0.9992Quintic 0.9993Exponential 0.6341Logarithmic 0.9687 The model that best fits Quintic regression
12. 12. Graph for best fit
13. 13. Properties of regressiony = -0.0006x5 + 0.0169x4 - 0.1926x3 + 0.859x2 + 1.4509x - 2.16 R² = 0.9993  Domain: {XER|X≥0}  Range: {YER|Y≥0}  X-intercept:  Y-intercept: -2.16
14. 14. 3 sets of Intervals
15. 15. Centered intervaly = -0.0006x5 + 0.0169x4 - 0.1926x3 + 0.859x2 + 1.4509x - 2.16 X=5 4≤x≤6 X=4 X=6 8.7732 13.1046 The instantaneous rate of change is 2.1657
16. 16. Verifying the degree of the functionDays Height1 0 2.8 12 2.8 3.2 -0.8 0.2 -0.43 6 3 -1.2 3.2 -1 2.84 1.6 -6.2 9 2 0.6 -3.4 -1.8 6.85 11 2.6 -1.2 3.4 1.6 -2.46 13.6 1.4 0.4 -1 0.6 1.47 15 1.8 -1 0.48 16.8 0.8 1 09 17.6 0.810 18.4
17. 17. Predictionf(11)= 12.191f(12)= 7.2732f(13)= -1.364f(15)= -37.21f(20)= -386.3The prediction is wrong because there is no such way thata plant can grow shorter as day passes.
18. 18. No direct sunlight(table)days height1 02 0.23 0.54 25 4.56 9.37 10.28 129 13.610 15.8
19. 19. Scatter plot
20. 20. Linear
22. 22. Cubic
23. 23. Quartic
24. 24. Quintic
25. 25. Exponential
26. 26. Logarithmic
27. 27. Best fit functionModel R2Linear 0.9577Quadratic 0.9652Cubic 0.9853Quartic 0.9883Quintic 0.9938Exponential 0.8824Logarithmic 0.793The model that best fits is Quintic regression
28. 28. Graph for best fit
29. 29. Properties of regressiony = 0.0048x5 - 0.1252x4 + 1.1201x3 - 3.8987x2 + 5.6573x - 2.62 Domain: Range: X-intercept: Y-intercept:
30. 30. 3 sets of intervals
31. 31. Centered intervaly = 0.0048x5 - 0.1252x4 + 1.1201x3 - 3.8987x2 + 5.6573x - 2.62 X=5 4≤x≤6 X=4 X=6 -43.078 -59.9098 The instantaneous rate of change is -8.4159
32. 32. Verifying the degree of thefunctionDays Height1 0.1 0.22 0.3 0.1 0.3 1.1 1.2 -1.33 0.6 -0.2 2.8 1.5 1.54 2.1 1 -9 2.5 1.3 2.3 -7.55 4.6 -6.2 18.5 4.8 116 -3.9 -16.9 9.4 0.9 4.8 0.9 -5.97 10.3 -1.1 -4 1.8 1.98 12.1 -0.2 0.8 1.69 13.7 0.6 2.210 15.9
33. 33. Predictionf(11)= 18.712f(12)= 37.634f(13)= 79.374f(15)= 292.12f(20)= 2839.8The prediction is unacceptable in real life situationbecause green beans cannot grow that much in just 20days.
34. 34. ConclusionBased on the analysis, the quartic regressionis the best fit for the growth of the greenbean with or without direct sunlight.
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