Explanation Given Information: A night club has a cover charge of $ 10 and get 660 patrons every night. The night club loses 30 patrons every night for each $ 1 they add to the cover charge. Formula used: For a parabola having a general form as, a x 2 + b x + c = y − d The x -intercepts are the points are the points on the parabola where it intersects the y -axis. A parabola may have either 2, 1 or 0 x -intercepts. To evaluate the x -intercept of the parabola of general equation a x 2 + b x + c = y − d , Now, substitute 0 for y in the equation. a x 2 + b x + c = 0 − d a x 2 + b x + c + d = 0 And, then the obtained quadratic equation is solved for x which provide the x -intercepts. Calculation: As it is provided in the question that a night club has a cover charge of $ 10 and get 660 patrons every night. The night club loses 30 patrons every night for each $ 1 they add to the cover charge. As for every dollar increased, in the cover charge the night loses 30 patrons. Therefore, the number of patrons lost is directly proportional to the numbers of dollars increased in the cover charge. Consider the number of patrons lost be represented by ‘ u ’ when there is a ‘ x ’ dollar increase in the cover charge then, u = 30 ⋅ x Consider final number of patrons in the night club be represented by ‘ w ’. Then, as the night club received 660 patrons every night on average. The final number of patrons after losing some by the increase in cover charge is given as, w = 660 − u = 660 − 30 x As the cover charge of the bight club is increased by ‘ x ’ dollars above the $ 10 . Then, the final cover charge is given by, Cover charge = 10 + x The revenue gained by the night club is equal to the multiplication of number of patrons with the cover charge as, revenue = number of patrons × cover charge Consider the revenue be represented as ‘ y ’ Now, Substitute 660 − 30 x as number of patrons and 10 + x as cover charge

1st Edition

ISBN: 9781259218859

Author: David Sobecki Professor, Brian A. Mercer

Publisher: McGraw-Hill Education

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Chapter 4.8, Problem 5A

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To calculate: The x-intercepts of the function which describes the average nightly revenue of a Night Club which has a cover charge of $10 and get 660 patrons every night. The night club loses 30 patrons every night for each $1 they add to the cover charge.

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Chapter 4.8, Problem 4A

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The x -intercepts of the function which describes the average nightly revenue of a Night Club which has a cover charge of $ 10 and get 660 patrons every night. The night club loses 30 patrons every night for each $ 1 they add to the cover charge.

Solution Summary: The author calculates the x -intercepts of the function which describes the average nightly revenue of a night club.

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To calculate: The x-intercepts of the function which describes the average nightly revenue of a Night Club which has a cover charge of $10 and get 660 patrons every night. The night club loses 30 patrons every night for each $1 they add to the cover charge.

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