Explanation Given Information: The weekly sales s ( t ) of cypods in the city state of Utarek on Mars fluctuated from a low of 5 units per week each February 1 ( t = 1 ) to a high of 35 units per week each August 1 ( t = 7 ) and t is time in months. Formula Used: The following generalized cosine function is used: f ( x ) = A cos [ ω ( x − β ) ] + C Where, A is the amplitude, the angular frequency is ω , the phase shift is β , the vertical offset is C. The time period P is calculated using the following formula, P = 2 π ω Calculation: Consider the lowest value of 5 units per week and highest value of 35 units per week. The weekly sales s ( t ) of cypods in the city state of Utarek on Mars is given by the cosine function as s ( t ) = A cos [ ω ( x − β ) ] + C . The vertical offset which is the height of the baseline is, C = low + high 2 = 5 + 35 2 = 40 2 = 20 The value of Amplitude which is the height of peak above the baseline is, A = High − offset = 35 − 20 = 15 Since, sales is in a year

7th Edition

ISBN: 9781337291248

Author: Waner, Stefan.

Publisher: Cengage Learning,

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Chapter 9.1, Problem 52E

To determine

To calculate: The cosine function to model the weekly sales s(t) of cypods in the city state of Utarek on Mars, which have fluctuated from a low of 5 units per week each February 1 (t=1) to a high of 35 units per week each August 1 (t=7) and t is time in months.

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Chapter 9 Solutions

Applied Calculus

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The cosine function to model the weekly sales s ( t ) of cypods in the city state of Utarek on Mars, which have fluctuated from a low of 5 units per week each February 1 ( t = 1 ) to a high of 35 units per week each August 1 ( t = 7 ) and t is time in months.

Solution Summary: The author calculates the cosine function to model the weekly sales of cypods in the city state of Utarek on Mars.

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To calculate: The cosine function to model the weekly sales s(t) of cypods in the city state of Utarek on Mars, which have fluctuated from a low of 5 units per week each February 1 (t=1) to a high of 35 units per week each August 1 (t=7) and t is time in months.

Chapter 9 Solutions