The table below shows the average monthly temperature in Wellington NZ from 1971 to 2000. The temperatures are in degrees Celsius. Month Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec °C 17.8 17.9 16.6 14.4 12.0 10.2 9.5 9.9 11.3 12.9 14.5 16.4 (a) Write a cosine function of the form A cos (Bt) + D to model the data. The input, t, to this function should be the month number (with t = 0 being January) and the output should be the average temperature for that month. (b) What are the units of the constants A, B, and D? (c) Explain what each of these three constants tells you about the temperatures that you are modeling. (d) Use a phase shift to fit a function of the form A sin(Bt+C) + D to the data, where t is the month number. (e) Use DESMOS to draw a scatterplot of the data. Compare the graphs of your two functions to this plot. Do they appear to model the data accurately?
The table below shows the average monthly temperature in Wellington NZ from 1971 to 2000. The temperatures are in degrees Celsius. Month Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec °C 17.8 17.9 16.6 14.4 12.0 10.2 9.5 9.9 11.3 12.9 14.5 16.4 (a) Write a cosine function of the form A cos (Bt) + D to model the data. The input, t, to this function should be the month number (with t = 0 being January) and the output should be the average temperature for that month. (b) What are the units of the constants A, B, and D? (c) Explain what each of these three constants tells you about the temperatures that you are modeling. (d) Use a phase shift to fit a function of the form A sin(Bt+C) + D to the data, where t is the month number. (e) Use DESMOS to draw a scatterplot of the data. Compare the graphs of your two functions to this plot. Do they appear to model the data accurately?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:(6) The table below shows the average monthly temperature in Wellington NZ from 1971 to
2000. The temperatures are in degrees Celsius.
Dec
Month Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov
°C 17.8 17.9 16.6 14.4 12.0 10.2 9.5 9.9 11.3 12.9 14.5 16.4
(a) Write a cosine function of the form A cos(Bt) + D to model the data. The input, t, to
this function should be the month number (with t = 0 being January) and the output
should be the average temperature for that month.
(b) What are the units of the constants A, B, and D?
(c) Explain what each of these three constants tells you about the temperatures that you
are modeling.
(d) Use a phase shift to fit a function of the form A sin(Bt+ C) + D to the data, where t
is the month number.
(e) Use DESMOS to draw a scatterplot of the data. Compare the graphs of your two
functions to this plot. Do they appear to model the data accurately?
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