document.write( "Question 639539: I have to extend a function table to 5,6,7
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\n" ); document.write( "\n" ); document.write( "Then simplify the the expressions.\r
\n" ); document.write( "\n" ); document.write( "Then write an equation that relates x and y when the value of x=15\r
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Algebra.Com's Answer #402786 by AnlytcPhil(1806)\"\" \"About 
You can put this solution on YOUR website!
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document.write( " X. Y                        Y\r\n" );
document.write( " 1. 1                    =   1\r\n" );
document.write( " 2. 1+2                  =   3\r\n" );
document.write( " 3. 1+2+4                =   7\r\n" );
document.write( " 4. 1+2+4+8              =  15\r\n" );
document.write( " 5. 1+2+4+8+16           =  31\r\n" );
document.write( " 6. 1+2+4+8+16+32        =  63\r\n" );
document.write( " 7. 1+2+4+8+16+32+64     = 127\r\n" );
document.write( " 8. 1+2+4+8+16+32+64+128 = 255\r\n" );
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document.write( "The simplified table looks like this:\r\n" );
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document.write( " X.   Y                        \r\n" );
document.write( " 1.   1\r\n" );
document.write( " 2.   3\r\n" );
document.write( " 3.   7\r\n" );
document.write( " 4.  15\r\n" );
document.write( " 5.  31\r\n" );
document.write( " 6.  63\r\n" );
document.write( " 7. 127\r\n" );
document.write( " 8. 255\r\n" );
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document.write( "Notice that each number in the Y column is 1 less than\r\n" );
document.write( "a power of 2.\r\n" );
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document.write( " X.   Y                        \r\n" );
document.write( " 1.   1 = 1 less than   2 = 21 - 1\r\n" );
document.write( " 2.   3 = 1 less than   4 = 22 - 1\r\n" );
document.write( " 3.   7 = 1 less than   8 = 23 - 1\r\n" );
document.write( " 4.  15 = 1 less than  16 = 24 - 1\r\n" );
document.write( " 5.  31 = 1 less than  32 = 25 - 1\r\n" );
document.write( " 6.  63 = 1 less than  63 = 26 - 1\r\n" );
document.write( " 7. 127 = 1 less than 128 = 27 - 1\r\n" );
document.write( " 8. 255 = 1 less than 256 = 28 - 1\r\n" );
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document.write( "  I'll remove the middle\r\n" );
document.write( "two columns to make it clearer:\r\n" );
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document.write( " X.   Y                        \r\n" );
document.write( " 1. 21 - 1\r\n" );
document.write( " 2. 22 - 1\r\n" );
document.write( " 3. 23 - 1\r\n" );
document.write( " 4. 24 - 1\r\n" );
document.write( " 5. 25 - 1\r\n" );
document.write( " 6. 26 - 1\r\n" );
document.write( " 7. 27 - 1\r\n" );
document.write( " 8. 28 - 1\r\n" );
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document.write( "Observing the pattern, we see that in every case the exponent\r\n" );
document.write( "of 2 is the same as the value of x.  So that will have to be the\r\n" );
document.write( "case when x=15, and we can jump to line 15\r\n" );
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document.write( "15. 215 - 1\r\n" );
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document.write( "Punching that out on a calculator gives 32767\r\n" );
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document.write( "A general equation that relates all values of x and y is\r\n" );
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document.write( " y = 2x - 1\r\n" );
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document.write( "Edwin
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