Crows Dropping Nuts Math Portfolio

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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

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) + d where a controls the curve of the model, b controls the shifts of the model, c is the rate of fall, and d is the horizontal asymptote. My function was f(x) = (47(x-1)-1.5) + 1. I chose this function because it seems to fit closely with the data provided. I used the parameters stated above to create the equation in my Graphic Display Calculator and adjusted based on how well it fit the data provided.  This is how my model appears by itself:

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And with the data points included:

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 ...

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