document.write( "Question 138289: For a certain strain of bacteria, k is 0.825 when t is measured in days. How long will it take 20 bacteria to increase to 2000? \n" ); document.write( "
Algebra.Com's Answer #101098 by ankor@dixie-net.com(22740)\"\" \"About 
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For a certain strain of bacteria, k is 0.825 when t is measured in days. How long will it take 20 bacteria to increase to 2000?
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\n" ); document.write( "Let t = number days for 20 to increase to 2000
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\n" ); document.write( "Use the formula:
\n" ); document.write( " Ao * 2^(t/k) = A
\n" ); document.write( "Where
\n" ); document.write( "A = resulting amt, 2000
\n" ); document.write( "Ao = initial amt, 20
\n" ); document.write( "t = time in days
\n" ); document.write( "k = .825
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\n" ); document.write( "20 * 2^(t/.825) = 2000
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\n" ); document.write( "divide both sides by 20 and you have:
\n" ); document.write( "2^(t/.825) = 100
\n" ); document.write( ":
\n" ); document.write( "Use common logs:
\n" ); document.write( "log(2^(t/.825)) = log(100)
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\n" ); document.write( "The log equiv of exponents:
\n" ); document.write( "(t/.825) * log(2) = log(100)
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\n" ); document.write( ".301(t/.825) = 2
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\n" ); document.write( "Multiply both sides by .825
\n" ); document.write( ".301t = .825 * 2
\n" ); document.write( ".301t = 1.65
\n" ); document.write( "t = \"1.65%2F.301\"
\n" ); document.write( "t = 5.482 days
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\n" ); document.write( "Check solution on a calc: enter 2^(5.482/.825) * 20 = .2001\r
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