Success in business depends on many factors. Buying habits of consumers, trends in fashion and taste, seasonal trends, the strength of the competition, and the condition of the national and international economies all affect the fortunes of a business. The result of these factors is that businesses often show a broad overall pattern of growth or decline superimposed on a continuing series of small ups and downs. Such business cycles can often be modeled by using trigonometric functions. Recall that sinusoidal trigonometric functions are periodic.
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)
1. Which of the following terms in the equation increases as t increases?
8
-6cos(πt/26)
t/52
cos(πt/26)
2. Which of the following terms in the equation increases and then decreases periodically as t increases?
6cos(πt/26)
πt/26
8 - πt/26
t/52
3. What are the maximum and minimum values of 6cos(πt/26)?
3π/13 and -3π/13
6 and -6
3πt/13 and -3πt/13
1 and -1
4. Which of the following accurately describes the sales cycle over several years?
Long-term cycles with long-term decline
Short-term cycles with short-term decline
Long-term cycles with short-term growth
Short-term cycles with long-term growth
I am pretty sure I am correct but I need to be sure I am doing this right so an answer would really help me out so I could check. There are more questions but I dont want to continue until I know what I am doing is right. Thanks so much!
