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4. The table shows the number C of cars in an office parking lot over the course of a work day. The time t is measured in hours, with t= 0 representing 7:00am. 11 10 8 9 12 0 t 1 6 2 4 7 3 5 34 12 C 13 67 92 108 86 110 100 82 52 15 75 a) You want to write a sinusoidal model for the data in the table without using a graphing calculator. Is it more convenient to model the data with a sine or cosine function? Explain. b) Write a sinusoidal model for the number C of cars as a function of the time t (in hours) without using a graphing calculator. Identify and explain how you calculated your values for the amplitude, period, horizontal shift, and vertical shift. c) Use a graphing calculator to write a sinusoidal model that gives C as a function of t. d) Using your model from part (c), at about what time(s) will there be 45 cars in the parking lot? Revised May 2016 Page 4

4. The table shows the number C of cars in an office parking lot over the course of a work day. The time t is measured in hours, with t= 0 representing 7:00am. 11 10 8 9 12 0 t 1 6 2 4 7 3 5 34 12 C 13 67 92 108 86 110 100 82 52 15 75 a) You want to write a sinusoidal model for the data in the table without using a graphing calculator. Is it more convenient to model the data with a sine or cosine function? Explain. b) Write a sinusoidal model for the number C of cars as a function of the time t (in hours) without using a graphing calculator. Identify and explain how you calculated your values for the amplitude, period, horizontal shift, and vertical shift. c) Use a graphing calculator to write a sinusoidal model that gives C as a function of t. d) Using your model from part (c), at about what time(s) will there be 45 cars in the parking lot? Revised May 2016 Page 4

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.6: Additional Trigonometric Graphs
Problem 78E
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4. The table shows the number C of cars in an office parking lot over the course of a work day. The time t is measured in hours, with t 0 representing 7:00am. 10 11 12 0. 1 3 6. 7 75 100 110 86 34 12 C 13 67 92 108 82 52 15 a) You want to write a sinusoidal model for the data in the table without using a graphing calculator. Is it more convenient to model the data with a sine or cosine function? Explain. b) Write a sinusoidal model for the number C of cars as a function of the time t (in hours) without using a graphing calculator. Identify and explain how you calculated your values for the amplitude, period, horizontal shift, and vertical shift. c) Use a graphing calculator to write a sinusoidal model that gives C as a function of t. d) Using your model from part (c), at about what time(s) will there be 45 cars in the parking lot? Revised May 2016 Page 4
Transcribed Image Text:4. The table shows the number C of cars in an office parking lot over the course of a work day. The time t is measured in hours, with t 0 representing 7:00am. 10 11 12 0. 1 3 6. 7 75 100 110 86 34 12 C 13 67 92 108 82 52 15 a) You want to write a sinusoidal model for the data in the table without using a graphing calculator. Is it more convenient to model the data with a sine or cosine function? Explain. b) Write a sinusoidal model for the number C of cars as a function of the time t (in hours) without using a graphing calculator. Identify and explain how you calculated your values for the amplitude, period, horizontal shift, and vertical shift. c) Use a graphing calculator to write a sinusoidal model that gives C as a function of t. d) Using your model from part (c), at about what time(s) will there be 45 cars in the parking lot? Revised May 2016 Page 4
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