Part a
1.
The percentage of NIH principal investigators
Age 36 and younger and age 66 and older
3.
4.
The function is a linear function
5.
This is a linear function because the lines pass
the vertical line test. Also looking that the slope or average rate of change,
the data will suggest that the line has a perceptible rate of change.
6.
Looking at the line (age 66 and Older) it is
also a mathematical model because there is always one output for every input.
Part b
1.
Percent of ad changes over time (2010)
|
Magazine Revenue Remains
Flat in 2010
|
||||
|
Percent of Change in Ad Pages Sold Overtime
|
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|
Year
|
% Change
|
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|
2000
|
10.1
|
|||
|
2001
|
-11.67
|
|||
|
2002
|
-3.19
|
|||
|
2003
|
-0.7
|
|||
|
2004
|
3.8
|
|||
|
2005
|
0.5
|
|||
|
2006
|
-0.1
|
|||
|
2007
|
-0.6
|
|||
|
2008
|
-11.7
|
|||
|
2009
|
-25.6
|
|||
|
2010
|
-0.1
|
|||
4.
The relationship is the comparison of
advertisement pages sold over the course of the year
5.
The function is not a linear function
6.
The function is linear because when modeled on a
graph the line produced passes the vertical line test. The slope or average
rate of change can be found by taking the x and y values or (year, percent
change) to find the slope. The graph produced by the data presented form a
graph that is not a function.
7.
But the function is not a mathematical model
because in some instances there are the same output values for different input
values. But since there are several input values corresponding to the same
output values, using function notation will produce similar numbers when this
instance comes up.
Good choice on the type of periodical graph that represents a linear function. It is an also interesting periodical as well.
ReplyDeleteI like the examples, that you picked. You also had good explanations. One things I would recommend is showing your calculations for the ROC, as you may want to check your work through working it out. Your non-linear example is presented clearly and is a good statistic to explain this concept on.
ReplyDeleteYou did good job in showing your work especially for the not function question and I like your choice for "the percent of change in ad pages sold overtime" it was well explained and I learn from it!
ReplyDeletebrooke,
ReplyDeleteyour first example is a nice one but could have been explained a little more accurately. for starters it is not a LINEAR function. it is a function and passes the VLT but it is not linear. secondly, there is not constant rate of change, if you had shown some calculations you would have seen that your notions would have been disproved by the ROC calculations at several intervals.
your second example is a good example in itself, but does not meet the criteria of a NON function. it passes the VLT if graphed, if the input values are time(year) and the output values are percent change.
please make sure that you understand the criteria for a function. a function can have more than one input paired with one output but visa versa is not a function. also, a mathematical model by definition is a function whose outputs depend on inputs. a function has exactly one output per input.
professor little