With the help of Mathews, Dr. Andersen constructed a timeline of the last 18 months. They mapped regions based on the intensity of his symptoms and found that there was a cyclical pattern. Question 3 (6 marks) 3) The cyclical pattern of symptoms is sinusoidal in nature. When graphed as a function of intensity, g(x) , and time, x in months, the function was very similar to f(x) = sinx . Dr. Andersen described shape of this graph, with reference to f(x) = sinx . Intensity is ranked on a scale of 0-10, where zero represents normal and ten represents full blown symptoms. The amplitude of the cyclical pattern is 5 and the equation of the axis of the curve is y = 5. The period of the function is 4 months. Using f(x) = sin x as a base function, the symptoms function has been horizontally translated 2 months to the right. a) (4 marks) Write a possible equation for the function g(x) . b) (2 marks) Sketch a graph of the function g(x) , by hand, on the interval 0Ex $ 18. 15 18 19 10 11 12 13 14 15 16 17 18 19 1|PageQuestion 4 (4 marks) Particular areas of this cyclical pattern are noteworthy. Use the equation found in question three. a) (2 marks) Determine algebraically when Mathews first ranked his intensity at 7.5. Give an exact answer. b) (1 mark) Determine when Mathews ranked his intensity at 7.5 for the third time. c) (1 mark) Determine how high Mathews ranked the intensity at 12 months. After gathering the data, the results from both tests in Part A and consultation with the relevant medical journals, the diagnosis was Small Intestinal Bacterial Overgrowth (SIBO). Small Intestinal Bacterial Overgrowth - The small intestine usually has about 10,000 bacteria per ml of fluid. In this disorder there are about 100, 000 bacteria per ml of fluid. This disease of the gastrointestinal tract is caused by a slowing of the normal muscle activity in the small intestine. This activity is responsible for routinely removing bacteria from the intestine