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. if needed, you can enter π=3. as 'pi' in your answer.

Step-by-step explanation:

Given that 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, where the months are numbered 1 through 12

Then minimum when x=10 and maximum when x = 4

Average = 44000 correspond to middle line

Amplitude =

Hence the function roughly would be

So we found out two values for A and D

To find values for B and C

The minimum of sine function corresponds to -pi/2 here it is 10 and maximum pi/2 here is 4.

Period = 12 months

So B = coefficient of X =

Because symmetrical about x=7 we have x-7 with a negative sign since min atx =10

arrange the equations with like terms in columns.

analyze the coefficients of x or y.

add the equations and solve for the remaining variable.

substitute the value into either equation and solve.

check the solution.

step-by-step explanation: