document.write( "Question 456862: You are a star basketball player and receive the following two offers. Which one should you choose and why? There are 82 regular season games in the NBA.)(Hint: Think about the function that each situation represents.)\r
\n" ); document.write( "\n" ); document.write( "Option 1: A one billion dollar signing bonus and 1 million dollars per game.\r
\n" ); document.write( "\n" ); document.write( "Option 2: A one penny signing bonus with salary to double each game. In other words the salary for the first game is 2 pennies, the salary for the second games is 4 pennies, and so on. \n" ); document.write( "
Algebra.Com's Answer #313624 by htmentor(1343)\"\" \"About 
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You are a star basketball player and receive the following two offers. Which one should you choose and why? There are 82 regular season games in the NBA.)(Hint: Think about the function that each situation represents.)\r
\n" ); document.write( "\n" ); document.write( "Option 1: A one billion dollar signing bonus and 1 million dollars per game.\r
\n" ); document.write( "\n" ); document.write( "Option 2: A one penny signing bonus with salary to double each game. In other words the salary for the first game is 2 pennies, the salary for the second games is 4 pennies, and so on.
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\n" ); document.write( "Option 1: The salaries for each consecutive game represent an arithmetic sequence with common difference = 1000000.
\n" ); document.write( "For example, the salary for the first 3 games will be: 1001000000, 1002000000, 1003000000.
\n" ); document.write( "The n-th term of an arithmetic sequence can be written:
\n" ); document.write( "\"a%5Bn%5D+=+a%5B1%5D+%2B+%28n-1%29d\", where d is the common difference
\n" ); document.write( "For simplicity, we will express our formula in millions of dollars.
\n" ); document.write( "So the salary for the n-th game will be \"a%5Bn%5D+=+1001+%2B+%28n-1%29%2A1\"
\n" ); document.write( "We can write the cumulative salary earned after game n as:
\n" ); document.write( "\"sum%28a%5Bi%5D%2C+i=1%2C+n%29\"
\n" ); document.write( "The sum of this series is \"%28n%2F2%29%28a%5B1%5D%2Ba%5Bn%5D%29\"
\n" ); document.write( "So the cumulative salary earned after the 82nd game will be:
\n" ); document.write( "\"a%5B82%5D+=+41%281001%2B1082%29+=+85403\" [in millions of dollars]
\n" ); document.write( "Option 2: In this case, we can describe the game salaries as a geometric
\n" ); document.write( "sequence with common ratio 2, since the salary doubles with each successive
\n" ); document.write( "game.
\n" ); document.write( "In general the sum of an arithmetic sequence can be written:
\n" ); document.write( "\"sum%28a+r%5Ek%2C+k=1%2Cn%29\"
\n" ); document.write( "The sum of this series is \"a%28r+-+r%5E%28n%2B1%29%29%2F%281-r%29\"
\n" ); document.write( "In this case, a = 1, and r = 2
\n" ); document.write( "Therefore the cumulative salary [in pennies] after game n can be written as
\n" ); document.write( "\"sum%282%5En%2C+k=1%2C+n%29\"
\n" ); document.write( "And the sum of this series is given by \"%282+-+2%5E83%29%2F%281-2%29+=+2%5E83+-+2\"
\n" ); document.write( "In dollars, the option 2 salary is \"%282%5E83+-+2%29%2F100+=+9.67E22\"
\n" ); document.write( "The option 1 salary, in dollars, is 85403*1E6 = 8.54E10
\n" ); document.write( "So, without question, the player should choose option 2 [I'd like to be his agent, and get 10% of that!]\r
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