Calculus
Calculus
10th Edition
ISBN: 9781285948133
Author: Ron Larson; Bruce H. Edwards
Publisher: Cengage Learning US
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Chapter P.4, Problem 14E

Temperature The table shows the normal daily high temperatures for Miami M and Syracuse S (in degrees Fahrenheit) for month t, with t = 1 corresponding to January. (Source: National Oceanic and Atmospheric Administration)

t 1 2 3 4 5 6
M 76.5 77.7 80.7 83.8 87.2 89.5
S 31.4 33.5 43.1 55.7 68.5 77.0
t 7 8 9 10 11 12
M 90.9 90.6 89.0 85.4 81.2 77.5
S 81.7 79.6 71.4 59.8 47.4 36.3

(a) A model for Miami is

M(t) = 83.70 + 7.46 sin(0.4912t –1.95).

Find a model for Syracuse.

(b) Use a graphing utility to plot the data and graph the model for Miami. How well does the model fit?

(c) Use a graphing utility to plot the data and graph the model for Syracuse. How well does the model fit?

(d) Use the models to estimate the average annual temperature in each city. Which term of the model did you use? Explain.

(e) What is the period of each model? Is it what you expected? Explain.

(f) Which city has a greater variability in temperature throughout the year? Which factor of the models determines this variability? Explain.

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Chapter P Solutions

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