From its past behavior, John knows that the value of a stock has a cyclical component that increases for the first three months of each year, falls for the next six, and rises again for the last...

Extracted text: From its past behavior, John knows that the value of a stock has a cyclical component that increases for the first three months of each year, falls for the next six, and rises again for the last three. In addition, inflation adds a linear component to the stock's price. John is seeking a model of the form f(t) = mt + b + A sin with t in months since Jan 1. He has the following data in the table: Jan 1 Apr 1 Jul 1 Price $20.00 $37.50 $35.00 $32.50 $50.00 Date Oct 1 Jan 1 a) What is the length of the period in his model? b) Determine two months when the Price is on the slanted midline. c) Find value of m, b, and A so that f fits the data.