Canned soups are consumed more during colder months and less during warmer months. A soup company estimates its sales of 16-oz cans of condensed soup to be at a maximum of 225 million during the 5th week of the year and at a minimum of 100 million during the 31st week of the year. (Note: This exercise corresponds to the subsection Characteristics of a Sine Function and requires use of the formulas for average value, amplitude, period, and horizontal shift to construct sine models rather than curve-fitting using technology.)

(a) Calculate the period and horizontal shift of the soup sales cycle. Use these values to calculate the parameters band c for a model of the form f(x) = a sin(bx + c) + d. (Assume that the horizontal shift is negative and the absolute value is less than the period. Round your answers to three decimal places when appropriate.) period weeks horizontal shift weeks
(b) Calculate the amplitude and average value of the soup sales cycle. amplitude million cans average value million cans
(c) Use the constants from parts (a) and (b) to construct the sine model for weekly soup sales in million cans on the xth week of the year, with data from 0 SXS 52. (Round all numerical values to three decimal places.) f(x) = Need Help?