Growth of a Green Bean

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.