Good Ol' Seagulls and Clams - Creating an equation based on data

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SUMMARY

The discussion centers on creating a mathematical model to analyze the relationship between the height of drops (x) and the number of drops required to break a clam (y). The user derived the equation y = 1/(0.045x) + 1 for the last six data points, identifying horizontal and vertical asymptotes. The challenge lies in formulating a piecewise function that accurately incorporates the first data point into the overall equation. The data provided includes specific height and drop values, essential for constructing the model.

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  • Familiarity with piecewise functions
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soccergirl14
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So pretty much, I was given data (see below) about seagulls dropping clams and the number of drops required to break the clam.

Height of drops (x)/number of drops (y)
1.7 / 42
2 / 21
2.9 / 10.3
4.1 / 6.8
5.6 /5.1
6.3 / 4.8
7 /4.4
8 /4.1
10 /3.7
13.9 /3.2



So for the last six points I created the equation y= 1/ (0.045x) +1 which showed there was a horizontal asymptote of 1 (because you can't have less than one drop), a vertical asymptote of 0 (because you can't drop the clam from a distance from less than zero), and no x-intercepts. I'm trying to create a piece wise function, but I'm having trouble getting the first point to relate to the other points in an equation.
 
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