document.write( "Question 1188459: yn= 1.05y(n-1) +2 and y(0) = 3. Find an explicit formula for y(n). \n" ); document.write( "
Algebra.Com's Answer #819604 by Edwin McCravy(20064)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "The other solution is incorrect.\r\n" );
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document.write( "A well-known theorem states that the general (explicit) formula for the recursion formula \r\n" );
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document.write( "\"y%5Bn%5D\"\"%22%22=%22%22\"\"A%2Ay%5Bn-1%5D%2BB\" has the form \"y%5Bn%5D\"\"%22%22=%22%22\"\"C%2AA%5En+%2B+D\"\r\n" );
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document.write( "We calculate y(1) = 5.15, y(2) = 7.4075, substitute it and A=1.05\r\n" );
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document.write( "\"5.15\"\"%22%22=%22%22\"\"C%2A1.05%5E1+%2B+D\"\r\n" );
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document.write( "\"D\"\"%22%22=%22%22\"\"5.15-1.05C\"\r\n" );
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document.write( "We calculate y(2) = 7.4075, substitute it and A=1.05\r\n" );
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document.write( "\"7.4075\"\"%22%22=%22%22\"\"C%2A1.05%5E2+%2B+D\"\r\n" );
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document.write( "\"7.4075\"\"%22%22=%22%22\"\"1.1025C+%2B+D\"\r\n" );
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document.write( "\"D\"\"%22%22=%22%22\"\"7.4075-1.1025C\"\r\n" );
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document.write( "Equating the expressions for D\r\n" );
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document.write( "\"5.15-1.05C\"\"%22%22=%22%22\"\"7.4075-1.1025C\"\r\n" );
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document.write( "\"0.0525C\"\"%22%22=%22%22\"\"2.2575\"\r\n" );
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document.write( "\"C\"\"%22%22=%22%22\"\"43\"\r\n" );
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document.write( "\"D\"\"%22%22=%22%22\"\"5.15-1.05%2843%29\"\r\n" );
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document.write( "\"D\"\"-40\"\r\n" );
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document.write( "General (explicit) formula\r\n" );
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document.write( "\"y%5Bn%5D\"\"%22%22=%22%22\"\"43%2A1.05%5EN-40\"\r\n" );
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document.write( "Edwin
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