Part a:
According to the Metropolitan Police Department of D.C., during the past 20 years the homicide rate within the district has decreased.
20-Year Homicide Trend
| 2013 | 2012 | 2011 | 2010 | 2009 | 2008 | 2007 | 2006 | 2005 | 2004 |
|---|---|---|---|---|---|---|---|---|---|
| 104* | 88 | 108 | 132 | 144 | 186 | 181 | 169 | 196 | 198 |
*The citywide 2013 homicide statistics include the 12 victims of the Washington Navy Yard shooting incident that occurred on September 16, 2013.
| 2003 | 2002 | 2001 | 2000 | 1999 | 1998 | 1997 | 1996 | 1995 | 1994 |
|---|---|---|---|---|---|---|---|---|---|
| 248 | 262 | 232 | 242 | 241 | 260 | 301 | 397 | 361 | 399 |
The rate of change is about: -15.52 homicides per year. Meaning, as time increases, homicides decrease by about 15.
This function is not linear because the average rate of change from interval to interval varies.
This function is not a mathematical model because the output is not dependent on the input.
Part b:
According to www.olympics.org, some of the total medals won by country for all the Olympic Games so far is as follows:
Armenia- 12
Bahamas- 12
Afghanistan- 2
British West Indies- 2
USA- 2653
This is not a function because some of the inputs (countries) have the same outputs (overall medal counts).
I found your post to be very interesting, specifically the statistics on DC's homicide rate. Although there is no greater comparision, 15 less homicides per year seems like a small number.
ReplyDeleteI think its interesting to see that not all rates of things are linear and that rates (like homicide) can fluctuate over a period of time like the function you have described.
ReplyDeleteWhen the input is a the country, and the out put is the number of medals received, wouldn't it still be a function?
ReplyDeleteyes, you are correct, uche. thank you for thinking about these posts and thoughtfully commenting.
DeleteIt was reassuring to see that as rate of time increases, homicides are decreasing. It also was very interesting to see that there was an mathematical decrease in the rate, even though it was not linear, it still is going down just not at an exact steady rate.
ReplyDeletevictoria,
ReplyDeleteyour first example is excellent! you did a great job of explaining why the relationship is a function and why it is not linear. although, you did not specify which quantities are inputs and outputs you still did a fine job.
your second example IS a function. uche is correct in her explanation of why the relationship would be a function. inputs can be paired with the same output and be a function, which is what you have here. however, inputs cannot be paired with more than one output.
professor little