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Crows Dropping Nuts

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Jimmy Cui

Crows Dropping Nuts

A reciprocal function is multiplicative inverse or reciprocal of a number x, denoted by  image03.pngimage03.pngor

x−1.The purpose of this portfolio is to help us explore the reciprocal function and discover that we can determine an equation through trial and error by making an educated guess through knowing the rule and patterns of the parameters.

Part 1- Large Nuts

Crows cannot break nuts since their beaks are weak, instead they will drop the nut repeatedly on a hard surface to open the nut.

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This is a graphical representation of the large nuts data using TI InterActive.

Relationship of Height of the drop vs. Number of drops for the Large Nuts


The variables in this data are that the height of the nut dropped affected the frequency, and this variable is put into an average. Another variable is the frequency of drops is also an average, where it is 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.

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The graph below is the combination of my equation and the large nut data.

Relationship of Height of the drop vs. Number of drops for the Large Nuts


The graph that I determined is similar to the data except that, it needs to be translated to the left a little bit and the rate of the drop and the horizontal asymptote should increase. The refined equation is f(x) = (70(x-.1)-1.85)+2


To find another function that models the data I used my graphing calculator to find the Power Regression. The Power function is (a)(xb) and the function that I found was (46.10)(x -1.15).

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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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