The sales for wetsuit manufacturer fluctuate throughout the

The sales for wetsuit manufacturer fluctuate throughout the year, with sales at their highest in mid-June at 160 wetsuits. At the lowest, they only sold 20 wetsuits in a month. (Use t =0 for Jan. 1) Find a function that gives the number of sales at time t. How many wetsuits would they sell in November?

Solution

1 jan to 15th jun for lets say year 2011 we have 166 days

(160 days , 160 wetsuits)

( 30 days, 20 wetsuits)

Let us use a sinusoidal function.

Period = 365 days

b = 2pi/365

Now , Let a is amplitude , x -a = 20

x +a = 160

-------- x = 90 ; a = 70

So, y = 70sin(2pi*t/365) + 90

Lets assume we have to find no. of wetsuits in mid November i.e. 15 th Nov , t = 319 days

So, y = 70sin(2pi*319/365) +90

= 40.18 = 40 wetsuits