document.write( "Question 39079: I need your help please. \r
\n" ); document.write( "\n" ); document.write( "The number of senior citizens (65 and over) in the United States in millions n years after 1990 can be estimated by using the formula.
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\n" ); document.write( "(US Bureau of the Census) The percentage of senior citizens living below level n years after 1990 can be estimated by using the formula.
\n" ); document.write( " p=0.25n + 12.2\r
\n" ); document.write( "\n" ); document.write( "a. How many senior citizens were there in 2000?
\n" ); document.write( "b. In what year will the percentage of seniors living below the poverty level reach 7%.
\n" ); document.write( "c. What is the first year in which can we expect both the number of seniors to be greater than 49 million and fewer than 7% living below the poverty level.\r
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Algebra.Com's Answer #24505 by AnlytcPhil(1806)\"\" \"About 
You can put this solution on YOUR website!
This problem is botched, either by you, your\r\n" );
document.write( "teacher or your textbook author.\r\n" );
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document.write( "The number of senior citizens (65 and over) in the United States in \r\n" );
document.write( "millions n years after 1990 can be estimated by using the formula.\r\n" );
document.write( "   s = 0.038 + 31.2  US Bureau of the Census)\r\n" );
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document.write( "You left off the n.  So I will assume the formula was supposed to\r\n" );
document.write( "be\r\n" );
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document.write( "   s = 0.038n + 21.2\r\n" );
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document.write( "a.  How many senior citizens were there in 2000?\r\n" );
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document.write( "2000 is 10 years after 1990, so plug 10 in the formula\r\n" );
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document.write( "   s = 0.038n + 31.2\r\n" );
document.write( "   s = 0.038(10) + 31.2\r\n" );
document.write( "   s = 31.58 million \r\n" );
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document.write( "The percentage of senior citizens living below [poverty] level \r\n" );
document.write( "n years after 1990 can be estimated by using the formula.\r\n" );
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document.write( "   p = 0.25n + 12.2\r\n" );
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document.write( "b.  In what year will the percentage of seniors living below the \r\n" );
document.write( "poverty level reach 7%.\r\n" );
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document.write( "There is something wrong here because according to that formula in\r\n" );
document.write( "1990, 0 years after 1990, the percentage was 12.2%. And, in 1991, the\r\n" );
document.write( "percentage was 12.45% and the percentage keeps going up after that.\r\n" );
document.write( "Thus is had already reached 12.2% in 1990.  So it must have reached\r\n" );
document.write( "7% long before 1990!  Be sure to ask your teacher if this problem was\r\n" );
document.write( "not in error.  But let's solve it anyway and see what happens:\r\n" );
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document.write( "Plug 7 in for p and solve for n\r\n" );
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document.write( "           p = 0.25n + 12.2\r\n" );
document.write( "           7 = 0.25n + 12.2\r\n" );
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document.write( " Clear of decimals by multiplying through by 100\r\n" );
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document.write( "         700 = 25n + 1220\r\n" );
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document.write( "  700 - 1220 = 25n\r\n" );
document.write( "        -520 = 25n\r\n" );
document.write( "     -520/25 = n\r\n" );
document.write( "       -20.8 = n\r\n" );
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document.write( "or approximately -21 years AFTER 1990, which means\r\n" );
document.write( "21 years BEFORE 1990 or way back in 1969.  \r\n" );
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document.write( "So it reached 7% way back in 1969 and it didn't\r\n" );
document.write( "reach 12.2% until 21 years later in 1990.\r\n" );
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document.write( "But surely this is not what you were given.  Be sure\r\n" );
document.write( "to ask your teacher.\r\n" );
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document.write( "c.  What is the first year in which can we expect both \r\n" );
document.write( "the number of seniors to be greater than 49 million and \r\n" );
document.write( "fewer than 7% living below the poverty level.\r\n" );
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document.write( "This is impossible, because it hasn't been below 7% since\r\n" );
document.write( "before 1969, and back then, using the formula that you left\r\n" );
document.write( "off the n in, and I guessed it was supposed to be after the\r\n" );
document.write( "0.038, substituting -21 for n (21 years before 1990),\r\n" );
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document.write( "   s = 0.038n + 31.2\r\n" );
document.write( "   s = 0.038(-21) + 31.2\r\n" );
document.write( "   s = 30.402 million\r\n" );
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document.write( "So back when the poverty level was below 7% there were\r\n" );
document.write( "fewer than 49 million -- in fact, less than 31 million.\r\n" );
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document.write( "Please check the assignment carefully and/or ask your\r\n" );
document.write( "teacher.\r\n" );
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document.write( "Edwin McCravy\r\n" );
document.write( "AnlytcPhil@aol.com
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