1 A particular leaf is comprised of 80 thousand cells. As the leaf grows, the number of cells grows at a daily rate of 6.5%. (a) Find a function f (x) = Aekx that models the number of cells (in thousands) after x days. (b) Use your function in part (a) to determine how long until the number of cells triples. 2 . Simplify tan (cos-1 ()) 3 . Find the inverse function of: f (x) = - 64 4 . A boat floating in the sea rises and falls with the waves. A sailor on the boat will also rise and fall with the boat. The function f(t) = 12sin ("t) + 8 measures the sailor's altitude above sea-level, in feet, where t is measured in seconds. (a) What is the maximum altitude of the sailor? (b) What is the length of time between successive periods of maximum altitude? (c) Find a time when the sailor is 3 feet below sea-level, Use an algebraic process to solve this problem and write your final answer as a decimal rounded to three places. 5 . Simplify as much as possible: log ()