AQR Unit 5: Using Functions in Models Length of Day Project. Name: Date:
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1 AQR Unit 5: Using Functions in Models Length of Project Name: : You may have noticed that during the winter the days are shorter and during the summer the days are longer. How much longer are days during the summer? Does the length of summer days change depending on the latitude of a place? You will investigate these questions using data from four different cities at four different latitudes: Houston, Texas 30 N latitude Philadelphia, Pennsylvania 40 N latitude Winnipeg, Manitoba, Canada 50 N latitude Porto Alegre, Brazil 30 S latitude The data in the tables for this activity describe the length of daylight for the year The data table is based on two assumptions: The length of daylight is defined as the amount of elapsed time between sunrise and sunset. Because 2009 is not a leap year, there are 365 days in the year. What is needed on the poster? 1. Scatterplots of data that is presented in the table, identifiable by city through the use of color or labels. 2. Answers to all questions including explanations and/or work 3. Final Summary sheet filled out for your cities.
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3 Group 1 : Houston and Philadelphia Here is the length of daylight by day number for Houston and Philadelphia. To make the graph easier, make January 1 = 1 and December 31 = 365. In addition, Houston Philadelphia Jan :17 9:23 Feb.1 10:48 10:11 March 1 11:34 11:19 Apr.1 12:29 12:41 May 1 13:20 13:56 June 1 13:57 14:46 July 1 14:01 14:57 Aug. 1 13:33 14:15 Sept.1 12:45 13:03 Oct.1 11:52 11:46 Nov.1 11:00 10:28 Dec.1 10:23 9:33 8. Determine the intersection points of the regression models for Houston and Philadelphia 10. When is there more daylight in Houston and Philadelphia? 11. What is the latitude in Houston and Philadelphia (read the intro)? 20 N: Guadalajara, Mexico compared to Houston? The winter months?
4 Group 2: Houston and Winnipeg Here is the length of daylight by day number for Houston and Winnipeg. To make the graph easier, make January 1 = 1 and December 31 = 365. In addition, Houston Winnipeg Jan :17 8:12 Feb.1 10:48 9:23 March 1 11:34 11:01 Apr.1 12:29 12:56 May 1 13:20 14:43 June 1 13:57 16:04 July 1 14:01 16:15 Aug. 1 13:33 15:11 Sept.1 12:45 13:28 Oct.1 11:52 11:37 Nov.1 11:00 9:46 Dec.1 10:23 8:25 8. Determine the intersection points of the regression models for Houston and Winnipeg. 10. When is there more daylight in Houston and Winnipeg? 11. What is the latitude in Houston and Winnipeg (read the intro)? 60 N: Seward, Alaska compared to Winnipeg? The winter months?
5 Group 3: Winnipeg and Philadelphia Here is the length of daylight by day number for Winnipeg and Philadelphia. To make the graph easier, make January 1 = 1 and December 31 = 365. In addition, Winnipeg Philadelphia Jan :12 9:23 Feb.1 9:23 10:11 March 1 11:01 11:19 Apr.1 12:56 12:41 May 1 14:43 13:56 June 1 16:04 14:46 July 1 16:15 14:57 Aug. 1 15:11 14:15 Sept.1 13:28 13:03 Oct.1 11:37 11:46 Nov.1 9:46 10:28 Dec.1 8:25 9:33 8. Determine the intersection points of the regression models for Winnipeg and Philadelphia. 10. When is there more daylight in Winnipeg and Philadelphia? 11. What is the latitude in Winnipeg and Philadelphia (read the intro)? 70 N: Barrow, Alaska compared to Winnipeg? The winter months?
6 Group 4: Porto Alegre and Philadelphia Here is the length of daylight by day number for Porto Alegre and Philadelphia. To make the graph easier, make January 1 = 1 and December 31 = 365. In addition, Porto Alegre Philadelphia Jan :03 9:23 Feb.1 13:29 10:11 March 1 12:42 11:19 Apr.1 11:45 12:41 May 1 10:55 13:56 June 1 10:19 14:46 July 1 10:15 14:57 Aug. 1 10:42 14:15 Sept.1 11:30 13:03 Oct.1 12:23 11:46 Nov.1 13:17 10:28 Dec.1 13:56 9:33 8. Determine the intersection points of the regression models for Porto Alegre and Philadelphia. 10. When is there more daylight in Porto Alegre and Philadelphia? 11. What is the latitude in Porto Alegre and Philadelphia (read the intro)? 40 S: Valdivia, Chile compared to Porto Alegre? The winter months?
7 Group 5: Porto Alegre and Winnipeg Here is the length of daylight by day number for Porto Alegre and Winnipeg. To make the graph easier, make January 1 = 1 and December 31 = 365. In addition, Porto Alegre Winnipeg Jan :03 8:12 Feb.1 13:29 9:23 March 1 12:42 11:01 Apr.1 11:45 12:56 May 1 10:55 14:43 June 1 10:19 16:04 July 1 10:15 16:15 Aug. 1 10:42 15:11 Sept.1 11:30 13:28 Oct.1 12:23 11:37 Nov.1 13:17 9:46 Dec.1 13:56 8:25 8. Determine the intersection points of the regression models for Porto Alegre and Winnipeg. 10. When is there more daylight in Porto Alegre and Winnipeg? 11. What is the latitude in Porto Alegre and Winnipeg (read the intro)? 20 S: Belo Horizonte, Brazil compared to Porto Alegre? The winter months?
8 Group 6: Porto Alegre and Houston Here is the length of daylight by day number for Porto Alegre and Houston. To make the graph easier, make January 1 = 1 and December 31 = 365. In addition, Porto Alegre Houston Jan :03 10:17 Feb.1 13:29 10:48 March 1 12:42 11:34 Apr.1 11:45 12:29 May 1 10:55 13:20 June 1 10:19 13:57 July 1 10:15 14:01 Aug. 1 10:42 13:33 Sept.1 11:30 12:45 Oct.1 12:23 11:52 Nov.1 13:17 11:00 Dec.1 13:56 10:23 8. Determine the intersection points of the regression models for Porto Alegre and Houston. 10. When is there more daylight in Porto Alegre and Houston? 11. What is the latitude in Porto Alegre and Houston (read the intro)? 50 S: Stanley, Falkland Islands compared to Porto Alegre? The winter months?
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