document.write( "Question 186794: This is a story problem and i have to find two equations.
\n" ); document.write( "one is linear and one is quadratic.
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\n" ); document.write( "\n" ); document.write( "\"Two very lucky twin brothers have very wealthy parents who offered them very generous allowances at the tender age of 8 years old. the boys had 2 choices. under Option 1, they could take a monthly allowance of $100 this year (year 0) and expect a $100 raise every year until they turn 18 (year 10). Under option 2 they could take a monthly allowance of $5 this year (year 0), and the amount would double every year until they turn 18 (year 10). What are the equations that would represent each option?\" \n" ); document.write( "
Algebra.Com's Answer #140040 by Edwin McCravy(20055)\"\" \"About 
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This is a story problem and i have to find two equations.
\n" ); document.write( "one is linear and one is quadratic.
\n" ); document.write( "here is the problem:
\n" ); document.write( "\"Two very lucky twin brothers have very wealthy parents who offered them very generous allowances at the tender age of 8 years old. the boys had 2 choices. under Option 1, they could take a monthly allowance of $100 this year (year 0) and expect a $100 raise every year until they turn 18 (year 10). Under option 2 they could take a monthly allowance of $5 this year (year 0), and the amount would double every year until they turn 18 (year 10). What are the equations that would represent each option?\"
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document.write( "The first, option 1, is indeed a linear equation.\r\n" );
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document.write( "A linear equation has a graph which is a straight line. A straight line\r\n" );
document.write( "is determined by two points.\r\n" );
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document.write( "for the year 1, their allowance is $100\r\n" );
document.write( "for the year 2, their allowance is $200\r\n" );
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document.write( "Let x = the year number and y = the allowance.\r\n" );
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document.write( "So the line which the graph of the equation goes through\r\n" );
document.write( "the two points (1,100), and (2,200)\r\n" );
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document.write( "First we find the slope, given by the slope formula \r\n" );
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document.write( "\"m=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29\"\r\n" );
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document.write( "\"m=%28200-100%29%2F%282-1%29\"\r\n" );
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document.write( "\"m=100%2F1\"\r\n" );
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document.write( "\"m=100\"\r\n" );
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document.write( "Now we substitute in the point-slope formula:\r\n" );
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document.write( "\"y-y%5B1%5D=m%28x-x%5B1%5D%29\"\r\n" );
document.write( "\"y-100=100%28x-1%29\"\r\n" );
document.write( "\"y-100=100x-100\"\r\n" );
document.write( "\"y=100x\"\r\n" );
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document.write( "So the 9th year their allowance will be found by\r\n" );
document.write( "substituting x=9, giving an allowance of y=$900.\r\n" );
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document.write( "I can't tell from the wording whether they get an allowance\r\n" );
document.write( "the 10th year or not, for it says \"until they are 18\".  Literally\r\n" );
document.write( "that means the last year they get an allowance is the 9th year.\r\n" );
document.write( "You'll have to ask your teacher whether they get an allowance on the\r\n" );
document.write( "10th year or not.  If so it will be $1000.\r\n" );
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document.write( "However option 2 is NOT a quadratic equation.  It is a geometric\r\n" );
document.write( "sequence.  The formula for the nth term of a geometric series is\r\n" );
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document.write( "\"a%5Bn%5D=a%5B1%5Dr%5E%28n-1%29\"\r\n" );
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document.write( "where the nth term is \"a%5Bn%5D\", \"a%5B1%5D=5\" and \"r=2\",\r\n" );
document.write( "since it doubles every year.  Substituting these:\r\n" );
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document.write( "For the 9th year, the allowance will be\r\n" );
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document.write( "\"a%5Bn%5D=a%5B1%5Dr%5E%28n-1%29\"\r\n" );
document.write( "\"a%5B9%5D=5%2A2%5E%289-1%29\"\r\n" );
document.write( "\"a%5B9%5D=5%2A2%5E8\"\r\n" );
document.write( "\"a%5B9%5D=5%2A256\"\r\n" );
document.write( "\"a%5B9%5D=1280\"\r\n" );
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document.write( "So the 9th year the allowance will be $1280.\r\n" );
document.write( "The 10th year it will be\r\n" );
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document.write( "\"a%5Bn%5D=a%5B1%5Dr%5E%28n-1%29\"\r\n" );
document.write( "\"a%5B9%5D=5%2A2%5E%2810-1%29\"\r\n" );
document.write( "\"a%5B9%5D=5%2A2%5E9\"\r\n" );
document.write( "\"a%5B9%5D=5%2A512\"\r\n" );
document.write( "\"a%5B9%5D=2560\"\r\n" );
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document.write( "So the 10th year the allowance would be $2560.\r\n" );
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document.write( "Comment:\r\n" );
document.write( "Maybe the first one was supposed to be done as\r\n" );
document.write( "an arithmetic series, which would give you the same\r\n" );
document.write( "answer as the linear way.  If so post again.  \r\n" );
document.write( "But option 2 is definitely a geometric sequence\r\n" );
document.write( "and is not a quadratic.  \r\n" );
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document.write( "Edwin
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