B. The Washington Capitals have always been best known for their star player, Alexander Ovechkin. Ovechkin has been a strong addition to the front line, having some of the highest total goals per season out of any player in the NHL. I have taken his total goals from the year 2005 to the year 2009 and analyzed his performance. My question is: Has Alex Ovechkin's performance improved throughout his career, or has he gotten worse?
C. Year # of Goals
2005 81
2006 82
2007 82
2008 79
2009 72
D.
(3, 82) and (5, 72): 5-3/72-82 = -2/10 or -1/5
(3, 82) and (4, 79): 4-3/79-82 = -1/3
(3, 82) and (3, 82): 3-1/82-81 = 2/1 or 2
Through these three ROC's, I can see that the majority of the time, the rate of change is negative, however it is positive at some parts of the graph as well. So, if we were only given these ROC's, we would still be able to tell that the graph goes both up and down. In terms of the situation, this means that Ovechkin has performed rather inconsistently, and that at some points in his career, he was improving, but at others, he was getting worse.
F. Shown in picture of part D
G. (3, 82) and (2, 83)
2-3/83-82 = -1
The IRC at the point (3, 82) is -1. Mathematically, this calculation means that at the point (3,82), the rate of change is -1. This rate of change is only applicable to the point (3,82) alone and is not applicable to the rest of the data. In this situation, this means that in the third year of Alex Ovechkin's career, his performance is decreasing.
H. We can know that the value in part G is the IRC because the point is taken from the tangent of that exact point. Since the point (3,82) is a point on the same line as (2,83), we know that their slopes are the same and therefore we can use these two points to determine the instantaneous rate of change for the point (3, 82)
Hey Caitlyn! I found the statistics very interesting for Alexander Ovechkin. I think your problem is very relatable to many other sport teams. This is because players usually tend to do better one year and worse the next and can have varying statistics. Also, good job on drawing your tangent line.
ReplyDeleteI liked the topic you picked to explore for this blog post! It was very interesting and you explained well how the IRC and ROC related to your problem specifically. Nice job with the graph as well. Well done!
ReplyDeleteThe topic you picked is very interesting and I choose one very similar. Your work all looks correct and is very well organized. Your graph is also very neat. The only thing I would be careful with is the statistics you got on ovi. Other than that good blog!
ReplyDeletehi, caitlyn,
ReplyDeleteyou chose a very interesting and easily understood topic. you example is very well organized and accessible. your table and graph look good and you drew an excellent tangent line!
however, in your graph, it looks as though one of the points you labeled on the graph does not match the same point that you used in your explanation of the IRC. additionally, your ARC calculations in part e are actually backwards. you divided the x's by the y's and it should be y2 - y1/x2 - x1. also, in part e, your last ARC calculation using (3, 82) and (3, 82) would be undefined, 0/0. you are correct that your IRC would be negative, but the values you calculated are incorrect. please take note of this. let me know if you have questions.
professor little