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# Coffee sales fluctuate with the weather, with a great deal more coffee sold in the winter than in the summer. For Joe's Diner, assume the function...

1. Coffee sales fluctuate with the weather, with a great deal more coffee sold in the winter than in the summer. For Joe's Diner, assume the function below models daily coffee sales in gallons.

2. The table shows the average number of daylight hours per month for Vancouver, B.C.

6. Coffee sales fluctuate with the weather, with a great dea l more coffee sold in the winter than i n the summer . For Joe's Diner , assume the function below models daily co ff ee s a l e s in gallons. I Y = G( t ) = 21 cos( I+ 0.74) + 291 where t is measured in days and 1 = 1 corresponds t o January I. (a) Determine: amplitude: _ _ _ _ _ period: _ _ m i dline: --- -- - - (b) Determi n e hically, to the nearest days , the dates between which there are l ess than 20 gallons of coffee sold. UseCALC S ! :intersect to fi nd the solution(s ). April, June , Sept . and Nov . h([lle 30 days. Feb. has 28 days. The rest of the months have 31 days. (c) What are the maximum and minimum gallons of coffee sold a t Joe's Diner and on what days do these occur? UseCALC 3 ! :minimum an d then 4 :m aximum to find the solution(s) . (d) Cha ll enge for bonus p oints: Solve part (b) symbolically ( algebraica ll y). You will need to clearly show all your steps, and there are several of them, including a substitut i on ; so, do your work on a separa te piece of paper and staple it to this worksheet . 7. The tab l e s hows the average number of daylight hours per month for Vancouver , B.C. s ourc - e: v ancouvcr cr 1matc at www . b cpaswor t . c o m 1 V · Ila 1 (a) Ent e r the data into youriST A 1 j menu under Lists I and 2 (or the equ i valent for T I -89s ). (b) Plot the data in an appropriate window aod use CALC !:SinReg to find a sinusoidal e4uation which models this data. Write the equation rounding a. b. c and d to 2 decimal places: (c) Using your equation , detem1ine the number of daylight hours in Vancouver, B.C. on September 15. ( d) The mood of persons with SAD syndrome (Seasonal Affective Disorder ) often depends on the number of daylight hours, where their mood is more cheerful when the daylight hours increase . Use your equation to estimate the number of days per year (usc I month30 . 5 days ) with more than 14 hrs of d a y l ight . Using a complete sentence, in t erpret the results.

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