Professor Little
Applied PreCalculus
8 February 2015
What's Your Function? Blog Post #2
http://www.washingtonpost.com/news/energy-environment/wp/2015/01/23/sorry-skeptics-nasa-and-noaa-were-right-about-the-2014-temperature-record/
(For the above image, I will focus on the table to the left). The above table was taken from the Washington Post, and shows the National Oceanic and Atmospheric Administration's predictions for the relationship between year and percentage probability of that year being the warmest year in history thus far. This table represents a function because for every output (the percentage), there is exactly one input (year). The function is not linear, however, because there is no average rate of change (or slope). The percentages do not change at consistent intervals. The function can be considered a mathematical model, however, because as the years pass, the probability of that year being warmest increases. Therefore, the year in time does affect the probability of that specific year being the warmest.
http://www.economist.com/news/briefing/21640316-children-rich-and-powerful-are-increasingly-well-suited-earning-wealth-and-power
The above graph, taken from the Economist, displays the relationship between SAT scores and family income. This graph does not represent a function because each SAT score range has multiple values (accounting for Reading, Math, and Writing scores), and each output (or income level) has multiple inputs (SAT score categories).
I love your part B analysis, they are clear and brief. Good job.
ReplyDeleteI like that you included what each input and output included specifically in the part B analysis.
ReplyDeleteGreat job!!! You are very clear and concise in your descriptions, so even someone who isn't very good at math (me) can understand. The only question I have is about the mathematical model portion of the first one: does probability come into effect when deciding whether it's considered a math model or not? I guess that it does clearly look like the temperature rises as the years go by, but the year does not directly influence what the temperature it will be (correct me if I'm wrong!)
ReplyDeletecarolyn,
Deleteyou make a great observation here, and i would also argue that the first example is not a mathematical model.
professor little
channing,
ReplyDeleteyour first example is a good one and you explained it's mathematical properties well. i would have to agree with carolyn that you could argue that it is not a mathematical model. the only other thing you forgot in the first part is to include a representation of the example using function notation.
your second example IS an example of three separate functions of reading, writing, math in relation to income. it does not fit the criteria for a non function.
professor little