You and your friends just move to Washington
DC. You guys know nothing about the weather here. So you decide to search on
the internet and get the following result.
Source: http://www.wunderground.com/history/airport/KDCA/2013/10/1/MonthlyHistory.html?
So, what is the instantaneous rate of
change for the temperature change during the seventh month?
Time(Months)
|
Temperature(F)
|
1
|
41
|
2
|
39
|
3
|
44
|
4
|
59
|
5
|
67
|
6
|
77
|
7
|
81
|
8
|
77
|
9
|
72
|
10
|
63
|
11
|
47
|
12
|
43
|
Average rate of Change (Slope):
From June to July
(77-81) / (6-7) = 4
From July to August
(81-77) / (7-8) = -4
From July to September
(81-72) / (7-9) = -4.5
I use the slope formula to figure it out. The
slope represents the average rate of change, which in the case is the average
change of temperature during each months. As we can see, the positive rate of change
means that the temperature is increasing. For example, the average temperature
increases from June to July, so the average rate of change increases. On the
other hand, the average temperature decreases from July to August and from July
to September. As a result, the average rate of change decreases.
A point on the tangent line will be
(2.5,50) and (5.5,70).
(70-50) / (5.5-2.5) = 6.6667
I find out the slope of the tangent line.
The tangent line passes through the point (7,81) since I use this point to find
the average rate of change. On the problem, it is 6.6667, this means that there
was a change of 6.6667 degrees increase.
I know that the value is the IRC because of
the calculations that I made, the answers are getting closer and closer to the
tangent line and the secant lines is moving closer and closer also. The value
is 6.6667 and it is also the slope of the tangent line.
Hey Matt,
ReplyDeleteI like that you looked at temperature for this project. It seems like you had good time with the project. What did you learn while doing this? What did you learn about the temperature and the months? Does anything have links ?
Tammy
hi, matt,
ReplyDeletei like that you chose a relevant topic. maybe i should employ this technique when i visit new cities!
you did a good job of calculating and creating graphics that are clear and aid in the understanding of your work. the wording in your explanation of IRC could have been a little more clear and should have included the units. in other words, you need to note that 6.6667 means that in july dc's average temperature is increasing at a rate of 6.6667 degrees per month. other than that clarity issue, good job.
prof little