document.write( "Question 381329: Please show how to and solve for x: 4 (x – 2) <= 6 (x + 5) \n" ); document.write( "
Algebra.Com's Answer #270480 by Edwin McCravy(20063)\"\" \"About 
You can put this solution on YOUR website!
3. How long, to the nearest tenth of a year, will it take $12,500 to grow to $20,000 at 6.5% annual interest compounded quarterly? (Use the formula for compound interest with n compoundings per year to solve for t.)
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document.write( "\"A\"\"%22%22=%22%22\"\"P%281%2Br%2Fn%29%5E%28nt%29\"\r\n" );
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document.write( "A = final amount = 20000\r\n" );
document.write( "P = beginning amount = 12500\r\n" );
document.write( "r = annual interest rate expressed as a decimal = .065\r\n" );
document.write( "n = number of times a year the interest is compounded = 4 (quarterly)\r\n" );
document.write( "t = number of years it takes P to grow to A = what we want to find\r\n" );
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document.write( "\"A\"\"%22%22=%22%22\"\"P%281%2Br%2Fn%29%5E%28n%2At%29\"\r\n" );
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document.write( "Take the log of both sides:\r\n" );
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document.write( "\"log%28%28A%29%29\"\"%22%22=%22%22\"\"log%28%28P%2A%281%2Br%2Fn%29%5E%28n%2At%29%29%29\"\r\n" );
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document.write( "Use this rule of logs:  \"log%28%28X%2AY%29%29=log%28%28X%29%29%2Blog%28%28Y%29%29\"\r\n" );
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document.write( "\"log%28%28A%29%29\"\"%22%22=%22%22\"\"log%28%28P%29%29%2Blog%28+%281%2Br%2Fn%29%5E%28n%2At%29%29+++\"\r\n" );
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document.write( "Subtract \"log%28%28P%29%29\" from both sides:\r\n" );
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document.write( "\"log%28%28A%29%29-log%28%28P%29%29\"\"%22%22=%22%22\"\"n%2At%2Alog%28+%281%2Br%2Fn%29%29+++\"\r\n" );
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document.write( "Divide both sides by \"n%2Alog%28%281%2Br%2Fn%29%29\"\r\n" );
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document.write( "\"%28log%28%28A%29%29-log%28%28P%29%29%29%2F%28n%2At%2Alog%28+%281%2Br%2Fn%29%29%29\"\"%22%22=%22%22\"\"%28n%2At%2Alog%28+%281%2Br%2Fn%29%29%29%2F%28n%2Alog%28+%281%2Br%2Fn%29%29%29\"\r\n" );
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document.write( "Cancel:\r\n" );
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document.write( "\"%28log%28%28A%29%29-log%28%28P%29%29%29%2F%28n%2At%2Alog%28+%281%2Br%2Fn%29%29%29\"\"%22%22=%22%22\"\r\n" );
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document.write( "\"%28log%28%28A%29%29-log%28%28P%29%29%29%2F%28n%2Alog%28+%281%2Br%2Fn%29%29%29\"\"%22%22=%22%22\"\"t\"\r\n" );
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document.write( "\"t\"\"%22%22=%22%22\"\"%28log%28%28A%29%29-log%28%28P%29%29%29%2F%28n%2Alog%28+%281%2Br%2Fn%29%29%29\"\r\n" );
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document.write( "Now substitute\r\n" );
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document.write( "A = final amount = 20000\r\n" );
document.write( "P = beginning amount = 12500\r\n" );
document.write( "r = annual interest rate expressed as a decimal = .065\r\n" );
document.write( "n = number of times a year the interest is compounded = 4 (quarterly)\r\n" );
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document.write( "\"t\"\"%22%22=%22%22\"\"%28log%28%2820000%29%29-log%28%2812500%29%29%29%2F%284%2Alog%28+%281%2B.065%2F4%29%29%29\"\r\n" );
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document.write( "\"t\"\"%22%22=%22%22\"\"%28log%28%2820000%29%29-log%28%2812500%29%29%29%2F%284%2Alog%28+%281%2B.065%2F4%29%29%29\"\r\n" );
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document.write( "\"t\"\"%22%22=%22%22\"\"7.289417683\"\r\n" );
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document.write( "That's over 7 years.  To find out how many months, multiply the\r\n" );
document.write( "fractional part .289417683 by 12, getting 3.473012194\r\n" );
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document.write( "So 7 years 3 months the amount will be less than $20000 and 7 years\r\n" );
document.write( "4 months it will be more than $20000.\r\n" );
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document.write( "Edwin
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