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Crows Dropping Nuts Math Portfolio

Extracts from this document...

Introduction


In this project, I will attempt to model the function of a group of crows dropping various size nuts from varying heights. The model will help to predict the number of drops it takes to break open nuts from even more heights.

The following table shows the average number of drops it takes to break open a large nut from varying heights.

Large Nuts

Height of drop (m)

1.7

2.0

2.9

4.1

5.6

6.3

7.0

8.0

10.0

13.9

Number of drops

42.0

21.0

10.3

6.8

5.1

4.8

4.4

4.1

3.7

3.2

When graphed in Excel, the points form this graph:

image00.png

To model this graph a power function can be used. There is an x variable and a y variable. For my model of the graph, I used a function with the following parameters: (a(x-b) c) + dwhere a controls the curve of the model, b controls the shifts of the model, c

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Middle

When graphed with Excel, a function of y = 46.096x-1.154 is found to be the best model of the data provided. Here it is graphed with comparison to my model:

image03.png

And with the data points:

image04.png

As you can see, the function produced by me and the function produced by technology only differ slightly. The technologically found function uses different parameters, but still has the same variables. Each function is not an exact fit to the data, but both models are fairly close.

The following table shows the average number of drops it takes to break open a medium nut from varying heights.

Medium Nuts

Height of drop (M)

1.5

2.0

3.0

4.0

5.0

6.0

7.0

8.0

10.0

15.0

Number of drops

-

-

27.1

18.3

12.2

11.1

7.4

7.6

5.8

3.6

When graphed with my large nut function, it appears as follows:

image05.png

My

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Conclusion

image08.png

My model/function now fits the small nut data better after this adjustment. This function is limited though. It would be better to create a whole new function to account for the medium nut size than to use the model from the large nut size. This new model/function would possibly create a better fit than using the large nut size function. Also, the data for the small nut seems more erroneous and spread out with lots of extremities. My model gives a good representation of the small nut data, but is not an exact fit, making this model limited.

In this project, I created functions that served as models for various sizes nuts. Using this data properly, one could possible predict the amount of drops it might take to crack open a nut from even more heights than are listed here.

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

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