• Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month

Crows Dropping Nuts Math Portfolio

Extracts from this document...


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)











Number of drops











When graphed in Excel, the points form this graph:


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

...read more.


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:


And with the data points:


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)











Number of drops











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



...read more.



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.

...read more.

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

Found what you're looking for?

  • Start learning 29% faster today
  • 150,000+ documents available
  • Just £6.99 a month

Not the one? Search for your essay title...
  • Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month

See related essaysSee related essays

Related International Baccalaureate Maths essays

  1. Extended Essay- Math

    ���+�1/4�Y���06l��ٳ����"���[email protected]��ҧ%=5h�*��4|U��AF�>��&^�-�(c)����� �hl��n�2jY�=�K{���.x�á³ï¿½ï¿½3)2jI'6]��Q�F�� ~��-{��u%Q�Q��� e��#����i�(r)]��-Ϧ�"P��p9�y�ڵf1/2> ��m1/4è¢a���Rj!�QÛ²e � �z��A���nuQ'K�VM�y��� �>eN���׿��w���_=� W�ZE��Ï߯_�1c�L�4)xS��"� ��x-��<���<%=���E�ƥ�-7n�<����(c)S��(tm)S__?h� "�)"j��tvNp,�� ä¬>����0NI����=��73/4��X4�#x���װaC,��Z�lY:4k+8'1/2}���V�p�@9T#�������F��Ü9�zd 9r$è�+W6o��kF�--e�|-zk�Ϣ'&�Ê~(c)...�""!�n����9�ӬX���/�:D�/�(c)\��Ì"t�'-� �N9�kihÚ��qQ0Û3A��z��...��w��}Ç-�m۶���]cÔ°qÞ���Uf�{j4�HD�>��F �~�)�v��l���"_z�%T�2�!C�4i�×�)t�z��m...n(c)��)� fC��֯^�'`��'�-w�u-"G�-'�t'g¦L(tm)2t�P:qL�p�d~{t]H��O� �"�'=)��>��St��I'8J��3 �Y�'�>knY��@ �3��8�0=�)�"�,XP3/4�f�[email protected]!���{y!�T*�}��5 q���DRJY��m�Z�+{��iy"�...��6�d��"x�pè���f 9�3벵�����...k�vLF�!e...�%c 1/2> �nDE"*Ä¢"j �s����P�:�5�7�s�N�E/_'qh�f4kÖi�֭[-UOE ���I�#->��WѢ��TV���a�a$�"d���] �Y%���@Y-��.�Å[ �Dp������ ":(r)� UQ`zj�� �"��2������H�n sb�ק7~�>Y�h'/]�"���ZpVN��c���9~�_$1/4Z�<z��0/3/4�b�YYb���β�ZE-"��...'�s�(sj��"�hDu1~�x�*N�0� Ö-z�h�x�]1/2O�>D(tm)��'?���O{���}�N4?'�pB�w�J���*X� � R,)Z���o ��� �'�ͷ�K{e0U_|1���;�'��7��Ö?���G�^_'��pÔ¨Q?��O}��1/2UO�Z�D �scO�Í��� 7�x# ��j���_�z3/4� �e�}����w���B���/�ܳh<e�ba-'R�SsBM!...�A��&!_6�Q���~���D��f"�Ï5"(r)(r)���Oç¤ï¿½(r)++*�1/4�O���;��[4cI -*�@,/�g#��g>�(tm)W_}�S�n��-�]���~7bÄ .�� �D_1/2��ʨ٣��%!��Ä�/7��� 9vh�]H.1/2�R��.]���O*4j�ׯ���}U"��fyy�|�I�d���[%ϯ��s�3/4���ld{� �YN�+�k(r)apz�m��j��� �����...k �"_a�w��FO�_��'�5c�K.��OQ �I�{�4}?...�1/4-_>�����,]��{:v�XV|9�"�>�hY���v"95��D%���[�:��a&��'Q�p�����o~�Rۧ��_�O��k�(r)�4:b��vZQ�a��k�1/2�=��7�x�-"�4-�Ô[5{t�$�Y��i���D�;��sq��W('�l�d�--��3��=����JÉD�...�~ G(c)1/4H������T���"�z��q��(r)@��d���#�1/4������o;p�@_���b�rk 3/4����u�D-�FR��...��'K�&������

  2. A logistic model

    and the excessively high (7.07x104)]. As previously explained, the population cannot remain that high and must thus stabilize itself, yet this search for stability only leads to another extreme value. The behaviour of the population is opposite to that of an equilibrium in the population (rate of birth=rate of death)

  1. Crows Dropping Nuts

    Using the GCD, I started with using PwrReG. To find the formula using PwrReg, press STAT, go to CALC, scroll down to A, and enter again. This will bring the calculator to the main screen with PwrReG, so now press enter again. Then the screen will give the values of "a" and "b". Plug the information into (y=)

  2. Crows dropping nuts

    Whereby low data values indicate that the points tend to be very close to the same value and the high data points are 'spread out' over a large range of values, this known as standard deviation as shown below. (Citationhttp://en.wikipedia.org/wiki/Standard_deviation)

  1. Creating a logistic model

    2.05 2 51250 1.2625 3 64703.125 0.85890625 4 55573.91846 1.132782446 5 62953.1593 0.911405221 6 57375.83806 1.078724858 7 61892.74277 0.943217717 8 58378.33153 1.048650054 9 61218.44052 0.963446784 10 58980.70967 1.03057871 11 60784.26368 0.976472089 12 59354.13697 1.019375891 13 60504.17625 0.984874712 14 59589.03319 1.012329004 15 60323.70664 0.990288801 16 59737.89111 1.007863267 17 60207.62608 0.993771218 18

  2. Math Portfolio: trigonometry investigation (circle trig)

    Based on this table we can see that there is relation between sin? and cos? from 0 to 90 degree. The example of sin30 equals to cos60 which the relation is that the theta is same. So the value of sin?

  1. Maths portfolio Crows dropping nuts

    Yet the graph can also not touch the axis, as the model will not work as well, as at 0m a y amount of times the nut has to be dropped. Therefore this creates a paradox. One function that could gimmick the original is Or the other function that could model this graph is the inverse exponential, where .

  2. Gold Medal heights IB IA- score 15

    Algebraic derived function : Converted to approx. Degrees : Regression by Graphmatica: h = 12.871 sin (0.0818t + 3.0456) + 213.5766 There are many similarities, solely based on the visual representation of the two model functions. Both models begin with a negative slope and hit a minimum point relatively the same area.

  • Over 160,000 pieces
    of student written work
  • Annotated by
    experienced teachers
  • Ideas and feedback to
    improve your own work