Question

8. Sales of the magazine 'Cheese!' fluctuate sinusoidally from a low of 250 magazines per week each February 1* to a high of 750 magazines per week each August 19. Model the weekly sales, S(t) of the Cheese! magazine, where time, t, is in months. a) Find a cosine equation for the magazine sales as a function of the time, t months. b) Draw a graph of the function for a minimum of a one- year period. c) Explain how the equation and graph would change if the maximum sales occurred in the first week of July instead of in the first week of August.

Answer 1

8 sales of a 250 magazine "Choose" functuate sinusoidally from low of magazines per week each February magazines 194 to a Per high of 750 ween each August 1st, f (2) = 250 F (8) = 750. Menimum Masimum. Amplitude = 750 750 - 250 2 250 Phase shifts - 500 enite up 750 + 250 and h = -8 werd 2 8 cents sight f(t) = (Amplitude) cos b(Ath) tk 250 cos b(tth) 4 500 250 cos 6 (-8) + 50

{С 1) — аясе Ь (а-2) - = cos b(-6) - - | 2) Ч ५ Сот cь = -1 СЬ Л Ь= 1 5 F(t) = 250 cos + (- 8) + 500

b) y = 500 250 + 2 + 8 14 c) It the martimum sale occurred in first week of 8 (71) = 750 y & F(l) would shibt I unt left y get) f (t+1) 250 cos T I(t+18) +500 awo Cos Ict-7) + 500