My experiment examines the temperature of Washington DC on
October 6th, 2014. The temperature was measured in degrees Fahrenheit
every 2 hours from 12am (0) to 4pm (16).
For our purposes we
want to find the temperature at exactly 10am.
Time
|
0
|
2
|
4
|
6
|
8
|
10
|
12
|
14
|
16
|
Temp.
|
57
|
53
|
51
|
50
|
52
|
59
|
68
|
75
|
77
|
Since I want to examine the IRC at exactly 10am I used the
point (10,59) to determine the slope at the locations using the formula
y2-y1/x2-x1
-
(10,59) to (12,68)
(68-59)/
(12-10) = 4.5
-
(10,59) to (8,52)
(59-52)/
(10-8) = 3.5
-
(10,59) to (14,75)
(75-59)/
(14-10) = 4
Since the slope for each of the points I
calculated was positive, it shows that the temperature between these points is
increasing. If any of the slopes had been negative, it would show that the
temperature was decreasing.
In order to find the IRC at exactly 10am,
you have to find the slope of the tangent line. To do this week take the coordinates
on either side of x=10 and put them into the derivative formula.
- (10,59) to (9,52)
(59-52)/
(10-9) =7
-(10,59) to (11, 65)
(65-59)/
(11-10) =6
By averaging out the two slopes from the
tangent line, it shows that the IRC of Exactly 10am should be approximately 6.5
(7+6)/2=6
The IRC shows that at exactly 10am the IRC
was approaching 6.5.
From using the values right next to x=10 we
see that are calculations get closer and closer to the IRC for 10am. Since we
cannot determine the IRC for exactly 10am because of the amount of data given
the next best option is to average the slope of the tangent line and find the
average between the two closest points.
Hey Avery! I liked how your scenario was very practical and it was interesting to see how the temperature slowly raises throughout the day. I can't view your graph, it could be a problem on my laptop, but I'm sure that looks good too. Nice job pointing out that the numbers get closer and closer to the IRC.
ReplyDeleteHey Avery! This was a very interesting example. I liked how you used a day to day example and explained your work thoroughly. I was able to follow the example easily! However, I also could not view the graph but it may be a laptop problem as well. Nice Job!
ReplyDeleteHey Avery! This was a good example and was very interesting. Your work all seems correct and your explanations are very good. Your blog post was very easy to follow. The graph also wouldn't load for me. Overall good work
ReplyDeletenice job, avery! i like that you used an example that we can all relate to! your calculations look good as well as your explanations. the only thing that i would add to your explanation of the IRC would be to denote what the units would be. so, at 10am, the temperature in washington dc is increasing at a rate of 6.5 degrees per hour.
ReplyDeleteother than that, great!
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