The function S(t) given below can be used to estimate the number of hours of daylight in Liberty Hill, TX for a given day of the year for 0 s t s 365 (t is in days and t = 0 is midnight on January 1). (calculator required) S(t) = - 1.95 cos ( (x + 24) ) + 12.15 hours/ day Use the given formula to find the following: a. What is the total number of daylight hours from the 100th day to the 200th day? b. Is the length of the day increasing or decreasing on the 100th day? Explain. c. What is the average number of hours of daylight from day 30 to day 250? d. On what day is the Summer Solstice (longest day of the year)? Explain