Green bean projectJason KohMHF4U
Under direct sun(table)
Days Height
1 0
2 2.8
3 6
4 9
5 11
6 13.6
7 15
8 16.8
9 17.6
10 18.4
Scatter plot
Linear
Quadratic
Cubic
Quartic
Quintic
Exponential
Logarithmic
Best fit function Model R2
Linear 0.9592
Quadratic 0.9982
Cubic 0.9992
Quartic 0.9992
Quintic 0.9993
Exponential 0.6341
Logarithmic 0.9687
The model that best fits Quintic regression
Graph for best fit
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
3 sets of Intervals 2.
==2
3.
=0.8
Centered interval y = -0.0006x5 + 0.0169x4 - 0.1926x3 +
0.859x2 + 1.4509x - 2.16 X=5 4≤x≤6
X=48.7732
X=613.1046
1. ==2.1657
The instantaneous rate of change is 2.1657
Verifying the degree of the function
Days Height
1 0
2 2.8
3 6
4 9
5 11
6 13.6
7 15
8 16.8
9 17.6
10 18.4
2.8
3.2
3
2
2.6
1.4
1.8
0.8
0.8
1
0.2
-1
0.6
-1.2
0.4
-1
0
-0.8
-1.2
1.6
-1.8
1.6
0.6
1
-0.4
2.8
-3.4
3.4
-1
0.4
3.2
-6.2
6.8
-2.4
1.4
Prediction f(11)= 12.191f(12)= 7.2732f(13)= -1.364f(15)= -37.21f(20)= -386.3
The prediction is wrong because there is no such way that a plant can grow shorter as day passes.
No direct sunlight(table)days height
1 0
2 0.2
3 0.5
4 2
5 4.5
6 9.3
7 10.2
8 12
9 13.6
10 15.8
Scatter plot
Linear
Quadratic
Cubic
Quartic
Quintic
Exponential
Logarithmic
Best fit function Model R2
Linear 0.9577
Quadratic 0.9652
Cubic 0.9853
Quartic 0.9883
Quintic 0.9938
Exponential 0.8824
Logarithmic 0.793
The model that best fits is Quintic regression
Graph for best fit
Properties of regression y = 0.0048x5 - 0.1252x4 + 1.1201x3 -
3.8987x2 + 5.6573x - 2.62 Domain: Range: X-intercept: Y-intercept:
3 sets of intervals
==1.5
==0.9
Centered interval y = 0.0048x5 - 0.1252x4 + 1.1201x3 -
3.8987x2 + 5.6573x - 2.62 X=5 4≤x≤6
X=4-43.078
X=6-59.9098
== -8.4159
The instantaneous rate of change is -8.4159
Verifying the degree of the function Days Heig
ht
1 0.1
2 0.3
3 0.6
4 2.1
5 4.6
6 9.4
7 10.3
8 12.1
9 13.7
10 15.9
0.2
0.3
1.5
2.5
4.8
0.9
1.8
1.6
2.2
0.1
1.2
1
2.3
-3.9
0.9
-0.2
0.6
1.1
-0.2
1.3
-6.2
4.8
-1.1
0.8
-1.3
1.5
-7.5
11
-5.9
1.9
2.8
-9
18.5
-16.9
-4
Prediction f(11)= 18.712f(12)= 37.634f(13)= 79.374f(15)= 292.12f(20)= 2839.8
The prediction is unacceptable in real life situation because green beans cannot grow that much in just 20 days.
Conclusion Based on the analysis, the quartic regression is the best fit for the growth of the green bean with or without direct sunlight.
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