PreCalculus: model sales w/ trig function; extrapolate; etc.

[sweetliljenny]

A company's sales are seasonal with the peak in mid-December and the lowest point in mid-June. The company makes $100,000 in sales in December, and only $20,000 in June.

(a) Find a trigonometric function, s = f(t), representing sales at time t months after mid-January

(b) What would you expect the sales to be for mid-April?

(c) Find the t-values for which s = 60,000. Interpret your answer.

 

[stapel]

The apex and nadir are six months apart, and are expected to cycle regularly every year. So what is the length of a period?

You are given the maximum and minimum sales amounts. What then would be the expected mean sales amount? (This gives you the vertical shift of your trig function.)

Given the mean value and the difference between the mean and the maximum, what then would be the amplitude?

When developing your trig function, you might want to start with a function that begins in December (at the max point) for convenience (and maybe use a cosine function), and then use a phase shift to start the function with "t = 0" indicating "January".

If you get stuck, please reply showing how far you have gotten. Thank you.

Eliz.

 

[sweetliljenny]

Amp. is going to be 100,000 - 20,000 = 80,000/2 = 40,000
Midline = 100,000 + 20,000 = 120,000 / 2 = 60,000

Period = 2pi / b
but we already know the period is 12 (months)

12 = 2pi / b ... cross multiply 12b = 2pi
divide 12 by both sides = 2pi/12 or = pi/6 = b

Now from there what do i do?