So.... What is your function?
Part A
The graph shown by this article exposes several sets of data that represent the billions of dollars spent on research and development by different countries. The graph displays a relatively constant research and development expenditures for Japan, Germany and U.K. Furthermore, China and US are making considerable changes. As we can appreciate china has made large investments in new technologies and it is expected to make larger investments in comparison to the U.S. The relationship of these graphs can be considered by a linear function because these increases in research and development may be dictated by a specific budget and also specific budgets increases planned for future years. Also it is a function because passes the Vertical Line test, which states that, in this case, for every year, there can only be one level of expenditures. Moreover, I can conclude that this can be a mathematical model because governments and companies use formulas in order to determine how much resources they can use depending on factors such as revenues and costs that might directly affect the resources available for research and development.
http://online.wsj.com/news/articles/SB10001424052702303819704579320544231396168
Part B.
The following graph is taken from the stock prices of Apple. There is a relationship between time and price given that for every factor of time, there is a specific price. Having said all that, I can say that the following graph is not a function because the output is not a function of time. Time does not determine the price of the stock. And even if we consider time as an accounting period where the company issues it’s financial statements periodically, we cannot attribute a function to determine these price levels, which would make everyone have an advantage in determining stock prices.
http://www.google.com/finance?q=Apple&ei=B-_ZUpjID43U6QH-ZQ
david,
ReplyDeleteI like the example that you used in the first example, but there are several issues with your explanation which I should point out. There are actually three separate functions here relative to time, the functions are not linear because the rate of change is not constant, i would not classify this as a math model since i don’t think that year has anything to do with how much government spending is being done.
for your second example, the graph is very interesting and useful, however, the relationship IS a function. not having a correlation between time and price means that the relationship is not a mathematical model, it does not mean that the relationship is not a function. in this relationship, there are no repeated input values and the graph passes the vertical line test, so it is a function.
please review the criteria for what constitutes and does not constitute a function.
professor little