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Maths portfolio Crows dropping nuts

Extracts from this document...

Introduction

Crows Dropping Nuts

SL Type 2

Name: Anis Mebarek

Teacher: Mr. Grimwood

Crows dropping nuts:

The table that is provided shows us the average of height and the number of times it takes to break the large nuts from that height.

Height of drop image02.pngimage02.png

1.7

2.0

2.9

4.1

5.6

6.3

7.0

8.0

10.0

13.9

Number of drops image09.pngimage09.png

42.0

21.0

10.3

6.8

5.1

4.8

4.4

4.1

3.7

3.2

Line graph depicting the table above, showing the frequency of drops by the height of the drop for a large nut.

image20.png

There numerous variables used for this graph. One such is the height at which the nut should be dropped affected the frequency, and this variable is put into an average. Another variable is the frequency of drops is also an average, where is it impossible to have 6.8 times of drops to open a nut. This has been converted into an average because it provides much clearer data, which could be put into one graph and distinguish the equation for it. Another variable is the size of the nut, where “large” is not very scientific and can vary in size and shape, which will consequently alter the frequency of drops it takes for it to crack open.

...read more.

Middle

image11.pngimage11.png

Equating the two to find a and b:

image10.png

(Minus)

image11.png

(Equals)

image12.png

image13.png

(Substituting a into the equation)

image14.png

image15.pngimage15.png 3.2

(Therefore)

image16.pngimage16.pngimage17.pngimage17.png

My model image18.pngimage18.pngagainst the current graph

image19.png

Height of drop

1.7

2

2.9

4.1

5.6

6.3

7

8

10

13.9

Number of drops

42

32

14.9

6.7

4

3.6

3.4

3.3

3.2

3.2

The curve of my graph is off-set to the bottom right therefore just coming of the line, also my model is not steep enough compared with the original. My model does cross through 3 points with the original graph showing how close it is. My model also shows that it is on the correct axis as the x axis asymptote, though not the y-axis asymptote. The accuracy of my graph is not too satisfying therefore using trial and error for image06.pngimage06.png will give me a better answer,

...read more.

Conclusion

image35.pngimage35.png.

My first model still does not come close to depicting the original graph as the difference in variables, which leads to differences in the asymptotes and the curvature of the graph. Though through using simultaneous equations the model image43.pngimage43.pngcomes very close to depicting the original, with four points matching and 2 not shows the accuracy of the graph. Through the limitation of the model is that its not crossing the rest of the points, where the curvature does not allow for the graph to include the two other points. This model will also cross the y-axis which will mean that the frequency will go in negative, hence in real life this model would not have worked.

...read more.

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