Part a:
http://search.proquest.com/docview/227989914/TextPlusGraphics/$N/0?accountid=8285
The function in this study describes the relationship between the willingness to pay for a certain price of potatoes and the number of important qualitative reasons that people are more willing or less willing to buy. Willingness to pay (WTP) is a function of the quantified qualitative reasons one might or might not buy potatoes multiplied by how important the reasons are, plus the normally distributed data gathered in this specific study when the mean is 0 and the standard deviation σ.
This study is far too subjective and singular to make the function linear, as the amount of importance people place on their respective values when it comes to buying potatoes is going to be vastly different between points based on this small data set. Because ß is multiplied by the input values, I can assume that ß represents the rate of change of the equation, and because it will not be regular, the function is non-linear.
This function is a mathematical model though, because the inputs have a great impact on the outputs, more than just recalling a year or another period of time.
Part b:
http://delivery.acm.org/10.1145/330000/320440/p9-chen.pdf?ip=147.9.222.63&id=320440&acc=ACTIVE%20SERVICE&key=4E7DC79309562578%2E4D4702B0C3E38B35%2E4D4702B0C3E38B35%2E4D4702B0C3E38B35&CFID=625152959&CFTOKEN=21289195&__acm__=1423455987_0004d8b7ccc216c4e8f403028ed3504d
This is a relationship between people's perceptions of entities and the number of things they imagine. It is not a function because the same input will have multiple outputs and there will be several overlapping data sets. It will therefore fail the vertical line test and be deemed not a function.
Hi Kira, I agree with you about the part 2, in a relationship that a function exists, must be one output per input, it can not be multiple outputs.
ReplyDeleteinteresting study and well done!
ReplyDeleteIt is very well written argument Kira! I definitely agree with you on your point in Part b where you identify that the relationship is not a function because one input can have multiple outputs, and this means it fails the vertical line test.
ReplyDeletekira,
ReplyDeleteyour first example is great! if you end up taking applied calculus with me, you will see that this is a real world application of derivatives called elasticity of demand. the only thing you forgot in your explanation here is to express the relationship using function notation.
i could not open the link for your second example, unfortunately, so i cannot assess your work on the second part.
professor little