Explanation Given: Three options are offered to a basketball player: A beginning salary of $1,700,000 with annual increase of $70,000 per year A beginning salary of $1,700,000 with annual increase of 2% per year A beginning salary of $1,500,000 with annual increase of 9% per year. Formula used: For an A.P. a 1 , a 2 , a 3 ,………, a n − 1 , a n is General term: a n = a 1 + ( n − 1 ) d Sum: S n = n ( a 1 + a n ) 2 Where a 1 is the first term, d is the common difference. And for the G.P. a , a r , a r 2 …………. a r n − 1 , a r n is General term: a n = a 1 r n − 1 Sum: S n = a 1 × ( 1 − r n ) 1 − r Where a is the first term, r is the common ratio. Calculation: Consider the first option: Annual salary of the player is increasing by a constant amount ($70,000) per year. So, the option can be modeled by an arithmetic sequence. Since, there is with annual increase of $70,000 so means we will have an arithmetic progression with common difference d = 70 , 000 Since, the beginning salary is $1,700,000. So, a 1 = 1 , 700 , 000 So, to find out what will be the amount paid after six year, use general term formula: a n = a 1 + ( n − 1 ) d Where, the first term is a 1 and common difference is d. Substitute a 1 = 1 , 700 , 000 , n = 6 and d = 70 , 000 , the 6 th term of the arithmetic sequence is, a 6 = 1 , 700 , 000 + ( 6 − 1 ) × 70 , 000 = 1 , 700 , 000 + 5 × 70 , 000 = 1 , 700 , 000 + 350 , 000 = 2 , 050 , 000 The sum of the first ‘ n’ terms of an arithmetic sequence, is given by S n = n 2 ( a 1 + a n ) Substitute n = 6 , a 1 = 1 , 700 , 000 and a 6 = 2 , 050 , 000 , the total amount of money over the 6-year contract will be, S 6 = 6 2 ( 1 , 700 , 000 + 2 , 050 , 000 ) = 3 × 3 , 750 , 000 = 11 , 250 , 000 Therefore, the total amount of money obtained by the first option in a 6-year contract is $11,250,000

Algebra & Trigonometry With Additional Material From College Algebra Essentials (custom Edition For Tidewater Community College)

7th Edition

ISBN: 9780536437273

Author: ROBERT BLITZER

Publisher: PEARSON

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Chapter 11.3, Problem 111E

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To calculate: Which of the three given options provides a basketball player the most amount of money over the 6-year contract and which provides the least? One advantage and one disadvantage of each option.

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Chapter 11.3, Problem 110E

Chapter 11.3, Problem 112E

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Chapter 11 Solutions

Algebra & Trigonometry With Additional Material From College Algebra Essentials (custom Edition For Tidewater Community College)

Ch. 11.1 - Fill in each blank so that the resulting statement...Ch. 11.1 - Fill in each blank so that the resulting statement...Ch. 11.1 - Fill in each blank so that the resulting statement...Ch. 11.1 - Fill in each blank so that the resulting statement...Ch. 11.1 - Prob. 5CVC Ch. 11.1 - Fill in each blank so that the resulting statement...Ch. 11.1 - Fill in each blank so that the resulting statement...Ch. 11.1 - Prob. 8CVC Ch. 11.1 - Prob. 1E Ch. 11.1 - Prob. 2E

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Which of the three given options provides a basketball player the most amount of money over the 6-year contract and which provides the least? One advantage and one disadvantage of each option.

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To calculate: Which of the three given options provides a basketball player the most amount of money over the 6-year contract and which provides the least? One advantage and one disadvantage of each option.

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