Part A.
The Great Jobs Puzzle: Working Hard or Hardly Working
http://www.economist.com/news/united-states/21594333-one-months-slip-does-not-slump-make-working-hard-or-hardly-working
I chose an article from the Economist which discusses the growth of employment (or the lack of it) in the month of December. The number of people who become employed each month is a function as this relationship passes the vertical line test when graphed. Furthermore, there is only one output (# of people employed) per input (month), another requirement for a function. For example, there were 74,000 people who found a Job in the month of December, not 74,000, 104,000, 70,000, etc.
This relationship is non-linear because the distance between intervals in the number of jobs created per month is not constant. In fact, one of the big issues this article discusses is the unpredictability of this function and its tendency to not be linear. In a healthy job market the function would approach a linear relationship and have a positive slope.
This function is not a mathematical model because while the input and output form a relationship, there is no formula to accurately describe that relationship. It's impossible to know how many jobs will be created in a given month based solely on the knowledge of what month it is.
Part B.
Aircraft Safety: Strike Out!
http://www.economist.com/news/science-and-technology/21594237-radar-stops-aircraft-colliding-each-other-it-should-be-used-stop-them
I chose another article from the Economist which discusses how technology can be used to track the movement of birds so jet aircraft can avoid sucking them into their engines. This technology can track individual birds and record their elevation so that aircraft can avoid them. This relationship, with elevation as an input and number of birds as an output, is not a function because multiple birds may be recorded at the same elevation (a flock). If you were to graph this relationship it would not pass the vertical line test because there would be multiple points at the same X-value.
I like that you managed to use an example in the first part that could act as both linear and non-linear. I actually hadn't, until now, given much thought to the idea that a graph or relationship could act in both a linear and non-linear fashion. Awesome job!
ReplyDeleteAlso, for unknown reason, your use of the word flock made me giggle.
I found your work to be both useful and detailed. I can't wait to read more of your posts.
ReplyDeleteBoth parts (A and B) I found interesting! Wish if there was a graph for part A though - after all, good job, I liked both =)
ReplyDeleteWell thought out, interesting answers to cool articles!
ReplyDeletesam,
ReplyDeletei really liked your first example and your explanations were excellent! i want to point out that there are two relationships in the first example that you used, seeing as how there are two lines graphed on the same grid. payroll is one function of time and household is another function of time.
your second example was of great interest to me personally, because i lost a friend in a plane crash due to birds getting into the plane engines. that aside, i believe that the relationship of number of birds with respect to elevation would be a function. number of birds would be a function of elevation and a different number of birds would correspond to different elevation values. hope this makes sense. otherwise, good job.
professor little