Question

The weekly sales in thousands of items of a product has a seasonal sales record
approximated by n = 53.6 + 19.3 sin (π*t)/24 (t is time in weeks with t = 1 referring to the first
week in the year). During which week(s) will the sales equal 63,250 items?

Answer 1

63.25 = 53.6 + 19.3 sin (pi t / 24)

sin(pi t/24) = (63.25 - 53.6)/19.3 =0.5

pi t / 24 = arc sin (0.5) = 30 o = (360/12)(2 pi) = pi / 6

t = 4

This model should use pi t / 26 so that pi (t=52)/26 = 2 pi, a full year cycle

Answer 2

Thank you. I totally understand 26 as the denominator

Answer 3

Very good.