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# Maths portfolio Crows dropping nuts

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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  1.7 2 2.9 4.1 5.6 6.3 7 8 10 13.9 Number of drops  42 21 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. 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.

Middle  Equating the two to find a and b: (Minus) (Equals)  (Substituting a into the equation)   3.2

(Therefore)    My model  against the current graph 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  will give me a better answer,

Conclusion  .

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  comes 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.

This student written piece of work is one of many that can be found in our International Baccalaureate Maths section.

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