The numbers of hours H of daylight in Denver, Colorado, on the 15th of each month starting with January are: 9.68, 10.72, 11.92, 13.25, 14.35, 14.97, 14.72, 13.73, 12.47, 11.18, 10.00, and 9.37. A model for the data is H(t) 12.13 + 2.77 sin(πt / 6 - 1.60) where t represents the month, with represents the month, with t = 1 corresponding to January.
(a) Use a graphing utility to graph the data and the model in the same viewing window.
(b) What is the period of the model? Is it what you expected? Explain.
(c) What is the amplitude of the model? What does it represent in the context of the problem?