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The economist for a large sporting-goods 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.)Short-term cycles with short-term decline
B.)Long-term cycles with long-term decline
C.)Long-term cycles with short-term growth
D.)Short-term cycles with long-term growth

  • precal -

    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 y-intercept of 8, and constantly increasing at the rate of (1/52).

    Can you deduce the answer from the above information?

  • precal -

    I'm thinking long term cycles with short term growth?

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