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Write-up


Title
Temperature Comparisons


Problem Statement
Collect temperatures measured in both Fahrenheit and Celsius so that you have 10 data points at least 10 Celsius degrees apart. Plot Fahrenheit vs. Celsius. Is this graph best described as a linear, exponential, or quadratic relationship? Explain your reasoning.


Problem setup

This investigation requests that we sample temperature relationships between Celsius and Fahrenheit. We are restricted to a minimum of 10 sample sets at least 10 degrees Celsius apart. We are then asked to plot the points and attempt to determine if they are linear, exponential, or quadratic.

 

Plans to Solve/Investigate the Problem

I will use Excel and an online metric to Fahrenheit conversion calculator to solve this problem. Using the conversion calculator, I will translate Celsius temperatures using 100 as the upper range, -100 as the lower range, and 10 as the interval. I will then place both Celsius and Fahrenheit data points into an Excel Chart. Upon completion, I will graph the points using a scatter plot, and come up with an equation using the trendline feature of Excel. If my R=1, then this formula will be exact.

 

Investigation/Exploration of the Problem

I created the excel spreadsheets as detailed above. I followed my procedural instructions, and ascertained that indeed my R=1 and my formula for converting Celsius to Fahrenheit is y = 1.8 x + 32. See Excel Spreadsheet below:

 

Celsius

Fahrenheit

100

212

90

194

80

176

70

158

60

140

50

122

40

104

30

86

20

68

10

50

0

32

-10

14

-20

-4

-30

-22

-40

-40

-50

-58

-60

-76

-70

-94

-80

-112

-90

-130

-100

-148

 

 

 

 

 

 

Extensions of the Problem

A possible extension would be to begin with Fahrenheit measurement and convert into Celsius. I will use the same procedure, and see what my results are. I theorize that there should be a converse relationship with my two equations.

 

Fahrenheit

Celsius

100

37.77778

90

32.22222

80

26.66667

70

21.11111

60

15.55556

50

10

40

4.444444

30

1.111111

20

-6.66667

10

-12.2222

0

-17.7778

-10

-23.3333

-20

-28.8889

-30

-34.4444

-40

-40

-50

-45.5556

-60

-51.1111

-70

-56.6667

-80

-62.2222

-90

-67.7778

-100

-73.3333

 

As seen in the sheet above, we do have an equation y = 0.5564x - 17.672, but our R value in just a bit

below 1 (R2 = 0.9998). I would make the assumption that this is due to rounding. (Probably why we were instructed to begin with Celsius.

Author & Contact
Jim Taylor
jtaylor1@rockdale.k12.ga.us

Link(s) to resources, references, lesson plans, and/or other materials
http://www.onlineconversion.com/temperature.htm


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