Tim is studying the climates of 3 cities around the world, each of which is 2300

Question

Tim is studying the climates of 3 cities around the world, each of which is 2300 to 2400 miles from the equator. He performs a sinusoidal regression on the data, which gives him a function for each city. Each function will return the average daily high temperature in degrees Fahrenheit for any given day of the year t, where t = 0 represents January 1, and t = 364 represents December 31. You may wish to plot these functions in your graphing calculator in radian mode: _____ Which city has the biggest temperature variation? (A) Los Angeles (B) Osaka (C) Buenos Aires _____ Which city is most likely to have snow in the winter? (A) Los Angeles (B) Osaka (C) Buenos Aires _____ Explain why the function for Buenos Aires has a positive horizontal shift as opposed to the negative shifts for Los Angeles and Osaka. During which months should Los Angeles and Osaka experience the same daily high temperature? _____ On which date is the high temperature most likely to be the same in all 3 cities? (A) March 15 (B) April 25 (C) May 25 (D) June 15 Even though it experiences the honest days in summer, Osaka is actually the coldest of the 3 cities, on average. Explain how the function allows you to make this conclusion.

Explanation / Answer

Ans(23):

Variation can be checked by amplitude

amplitude for Los Angeles, USA= 8.0686
amplitude for Osaka, Japan= 20.71
amplitude for Buenos Aires, Argentina= 13.03
maximum among them is 20.71
so answer is Osaka, Japan

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