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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