Decision Making Strategies Model With Peanuts

Sharimistha Santra
March 2015
Decision-Making Strategies Model with Peanuts

Animals are always seen to apply decision-making strategies to improve their chances in survival. Some scientists on Mandarte Island in British Columbia observed northwestern crows. The crows over there were attempting to break the whelk’s shell by dropping it from a height of about 5 meters. According to the scientist, the crows were very persistent in flying up and down repeatedly to drop the same whelk until it finally broke.
The aim of this exploration is to model the decision-making strategies used by the crows to determine an optimal dropping height. We collected some experimental data by dropping some peanuts at different heights. The heights that we choose

The equation that I chose is y=ax^2+bx+c. Although it had a horizontal asymptote, the graph was a parabola, which is irrelevant for this data plot. The model is half correct because is shows as the dropping height increased the number of drops required to break the peanuts decreased, but it is half incorrect because after a certain height the number of drops increases even when the dropping height increases. The parameters for this model were calculated by the desmos application. The parameter of ‘a’ was 0.0121, the parameter for ‘b’ was -1.17 and the parameter for ‘c’ was 29.9. The correlation of the data points and the model was strong as the value calculated by the desmos application was 0.924. The high value show that the model and the data points have a strong non-linear relation. The quadratic graph doesn’t work as a model for this exploration because as explained above because after a certain height it increases the no. of drops required to break the peanut, which is incorrect as the data is inversely proportional to each

The equation that I used was y=(ax+b)/(cx+d)+1. This model has both the horizontal and the vertical asymptote. The horizontal asymptote is 0 and the vertical asymptote is also 0. This equation is the best model for the decision-making strategies exploration. This model also has a reflection on Quadrant III but that is not necessary for this exploration as both the x and y variable have to be positive. The parameters are calculated directly by the desmos application. For this equation, there are four parameters; a, b, c, and d. But only two are necessary, parameter ‘a’ and parameter ‘b’ because those are the positive parameters and the other (c and d) refers to the negative parameter. Therefore, the parameter of ‘a’ was -6.07, the parameter of ‘b’ was 759, the parameter of ‘c’ was 6.64 and the parameter of ‘d’ was -58.4. The correlation between the model and the data points were very strong for this equation. The correlation calculated by the desmos application was 0.998, which shows that the model and the data points have a very strong non-linear