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 + As sin with t in months since Jan 1. He has the following data: Date Jan 1 Aprl Jul1 Oct Jan 1 Price S20.00 S37.50 S35.00 S32.50 S50.00 (a) Find values of m, b, and A so thatf fits the data. (b) During which month(s) does this stock appreciate the most? (c) During what period cach year is this stock actually losing value?