631 6.3 Graphs of the Sine and Cosine Functions (Modeling) Tides for Kahului Harbor The chart shows the tides for Kahului Harbor (on the island of Maui, Hawaii). To identify high and low tides and times for other Maui areas, the following adjustments must be made. Hana: High, +40 min, +0.1 ft; Low, +18 min, -0.2 ft Makena: High, +1:21, -0.5 ft; Low, +1:09, -0.2 ft Maalaea: High, +1:52, -0.1 ft; Low, +1:19, -0.2 ft Lahaina: High, +1:18, -0.2 ft; Low, +1:01, -0.1 ft JANUARY 19 20 21 22 6 A.M. Noon 6 P.M. 6 A.M. Noon 6 P.M. 6 A.M. Noon 6 P.M. 6 A.M. Noon 6 P.M. 0 1 2 3 0 1 2 3 Feet Feet Data from Maui News. Original chart prepared by Edward K. Noda and Associates. Use the graph to approximate each answer. 49. The graph is an example of a periodic function. What is the period (in hours)? 50. What is the amplitude? 51. At what time on January 20 was low tide at Kahului? What was the height then? 52. At what time on January 20 was low tide at Maalaea? What was the height then? 53. At what time on January 22 was high tide at Lahaina? What was the height then? (Modeling) Solve each problem. 54. Activity of a Nocturnal Animal Many activities of living organisms are periodic. For example, the graph at the right below shows the time that a certain nocturnal animal begins its evening activity. (a) Find the amplitude of this graph. (b) Find the period. Apr Jun Aug Oct Dec Feb Apr 6:30 7:00 7:30 8:00 4:00 4:30 5:00 5:30 Time p.m. Month Activity of a Nocturnal Animal 55. Atmospheric Carbon Dioxide At Mauna Loa, Hawaii, atmospheric carbon dioxide levels in parts per million (ppm) were measured regularly, beginning in 1958. The function L1x2 = 0.022x2 + 0.55x + 316 + 3.5 sin 2px can be used to model these levels, where x is in years and x = 0 corresponds to 1960. (Data from Nilsson, A., Greenhouse Earth, John Wiley and Sons.) (a) Graph L in the window 315, 454 by 3325, 3854. (b) When do the seasonal maximum and minimum carbon dioxide levels occur? (c) L is the sum of a quadratic function and a sine function. What is the significance of each of these functions?
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