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Problem 78 Easy Difficulty

Data Analysis The table shows the average daily high temperatures for Nantucket, Massachusetts and Athens, Georgia (in degrees Fahrenheit) for month with corresponding to January.
(a) A model for the temperature in Nantucket is given by
$$
N(t)=58+19 \sin \left(\frac{2 \pi t}{11}-\frac{21 \pi}{25}\right)
$$
Find a trigonometric model for Athens.
(b) Use a graphing utility to graph the dathend the model for the temperatures in Nantucket in the same viewing window. How well does the model fit the data?
(c) Use a graphing utility to graph the data and the model for the temperatures in Athens in the same viewing window. How well does the model fit the data?
(d) Use the models to estimate the average daily high temperature in each city. Which term of the models did you use? Explain.
(e) Which city has the greater variability in temperature throughout the year? Which factor of the models determines this variability? Explain.

Answer

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Video Transcript

the first one is the equation given to me off Nantucket. The temperature in the ticket and the second one is the equation for Athens that I've found using this graph. You you can see I've used a sine function. Why is equal toe a sign? B X plus C plus day? And these are the values that I found for A, B, C and D. Let's come back. The question says. What is the average daily high temperature in each city? Well, the Everest can be given by these constant terms 58 64.2. Then what is the period off each of these? The period for the first one. The period for this one is to buy, divided by the coefficient of tea that is two pi by 11 to buy by 11. Or this turns out to be 11. And what is the coefficient for this one? UH, 0.37 So the time period will become to buy, divided by 0.37 Now, what is to buy? Divided by 0.37 divided by 0.37 it is 16.98 This is coming out to be. This value is coming out to be 16.98 So this is my time period for the second one. Now, which term is going to show me the variability? It's this. The coefficient off the function is going to show me the variability. So the variability for the first equation, although for the first curve, is 19 and the variability for the second one is 25 0.9, which means the variability in the temperature off Athens is more The coefficient off the function will show the variability because it is going toe. Tell us what the amplitude is. This is a ransom.

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