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jfg4707
Average Member

USA
19 Posts

Posted - 10/05/2007 :  14:15:33  Show Profile
Hi,

I would like to know if I have answered the following questions correctly.

Problem
A company sells S(t) thousand electric blankets in month t (with t=0 being January), where the approximate value of S(t) is given by S(t) = 72.25 + 41.5 sin(/6t + /2). Find the function's period and amplitude and explain their practical significance. Also, when does the period begin for this function?

Solution
The amplitude is |A| = 41.5. It's practical significance is that it represents the averge sales over the year.

The period is given by P = 2/B = (2)/(/6) = 12. The period tells us the number of months for the sales to go through a complete cycle, i.e., 12 months.

The function has a horizontal shift to the left given by C/B = (-/2)/(/6) = -3. Hence, the period begins in October.

Thank you for any help you can give me.
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tkhunny
Advanced Member

USA
1001 Posts

Posted - 10/05/2007 :  14:45:26  Show Profile
Everything but Amplitude. Try that again. I think 72.25 is the average sales. 41.5 dances around 72.25.
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jfg4707
Average Member

USA
19 Posts

Posted - 10/05/2007 :  15:27:53  Show Profile
Thank you, tkhunny.

Yes, the midline (or line of oscillation) is the average sales for the year. The amplitude, 41.5, then, is amount of variation from that averge in a positive and a negative direction (or, the high and low variation from the average).
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