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

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:

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