Norman and Lydia retired and moved to the Caribbean, where they enjoyed the beau

Question

Norman and Lydia retired and moved to the Caribbean, where they enjoyed the beautiful sunrises each morning. The time sunrise occurred on six days during the year is recorded in the table. 3. Aruba 1st Day of Month Jan. 1 Mar. 1 May 1 July 1 Oct. 1 Dec. 1 Time of Sunrise (a.m.) 7:02 6:45 621 6:14 6:44 7:03 Day of Year (#) 60 Time of Sunrise 7.033 6.75 a) Complete the table above by converting the date to the number of the day and the time to the decimal equivalent on the 24-hour clock. (2 marks) Use technology to plot the points and determine the sinusoidal regression equation that best models the time of sunrise each day over the year. Sketch the graph below or include a printout. Include labels and units on the graph. b)

Explanation / Answer

a) May1 -> 31+28+31+30 = 120+1 = 121

6:21 -> 6+21/60 = 6+0.35 = 6.35

July1 -> 120+31+30 = 181+1 = 182

6:14 -> 6+14/60 = 6+0.23 = 6.23

Oct.1 -> 181+31+31+30=273+1 = 274

6:44 -> 6+44/60 = 6+0.73 = 6.73

Dec.1 -> 273+30 = 303+1 = 304

7:03 -> 7+3/60 = 7+0.05 = 7.05

c) Average time of sunrise during the year :

(7.033+6.75+6.35+6.23+6.73+7.05)/6 = 6.6905

d) Time of earliest sunrise = 6.23 and it occurs on 182th day of year

Time of latest sunrise = 7.05 and it occurs on 304th day of year

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