Over the past several years, the owner of a boutique on aspen avenue has observed a pattern in the amount of revenue for the store. the revenue reaches a maximum of about $ 59000 in april and a minimum of about $ 29000 in october. suppose the months are numbered 1 through 12, and write a function of the form f(x)=asin(b[x−c])+d that models the boutique's revenue during the year, where x corresponds to the month.

Step-by-step explanation:

Given, the function that shows the revenue.

,

Where, x corresponds to the month.

∵  Revenue reaches a maximum of about $ 59000 in April and a minimum of about $ 29000 in October,

i.e. the maximum value f(x) is $ 59000 when x = 4,

And,  the minimum value f(x) is $ 29000 when x = 10,

So, the amplitude,

The minimum of sine function corresponds to , here it is 10 and maximum , here it is 4.

Period = 12 months,

But we know period =

∵ ,

Thus, f(x) is symmetrical about x=7,

⇒ C = 7,

Also, f(x) is minimum at x = 10,

So, A = - 15000,

Hence, the required function would be,