Posted by Anonymous on Wednesday, August 25, 2010 at 11:13pm.
The economist for a large sportinggoods manufacturer developed the following function to model the company's sales, where S is sales in millions of dollars and t is the week of the year, beginning January 1 of each year:
S = 8 + t/52 – 6cos(πt/26)
Which of the following accurately describes the sales cycle over several years?
A.)Shortterm cycles with shortterm decline
B.)Longterm cycles with longterm decline
C.)Longterm cycles with shortterm growth
D.)Shortterm cycles with longterm growth

precal  MathMate, Thursday, August 26, 2010 at 8:29am
If we look at the cosine function which can be written as
cos((t/52)2π), we conclude the cycles are over periods of 52 weeks, meaning yearly cycles.
The first two terms represent a straight line with a yintercept of 8, and constantly increasing at the rate of (1/52).
Can you deduce the answer from the above information?

precal  Anonymous, Thursday, August 26, 2010 at 4:13pm
I'm thinking long term cycles with short term growth?
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