document.write( "Question 1188652: A bacteria culture starts with 280 bacteria and grows at a rate proportional to its size. After 5 hours there will be 1400 bacteria. \r
\n" ); document.write( "\n" ); document.write( "A. What will the population be after 4 hours?\r
\n" ); document.write( "\n" ); document.write( "B. How long will it take the population to reach 2630? Give your answer accurate to 2 decimal places. \n" ); document.write( "

Algebra.Com's Answer #819788 by ikleyn(52781) $\"\"$ $\"About$

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\n" ); document.write( "A bacteria culture starts with 280 bacteria and grows at a rate proportional to its size.
\n" ); document.write( "After 5 hours there will be 1400 bacteria.
\n" ); document.write( "A. What will the population be after 4 hours?
\n" ); document.write( "B. How long will it take the population to reach 2630? Give your answer accurate to 2 decimal places.
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document.write( "Write the exponential growth function with arbitrary base b\r\n" );
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document.write( "    B(t) = ,\r\n" );
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document.write( "where \"t\" is the time in hours.\r\n" );
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document.write( "I use the multiplier 280, because it is the original number of bacteria at t = 0.\r\n" );
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document.write( "To find the base \"b\" value, write an equation as you read the problem\r\n" );
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document.write( "    1400 = ,\r\n" );
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document.write( "or\r\n" );
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document.write( "     = \r\n" );
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document.write( "        5  = .\r\n" );
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document.write( "From here, you find  b =  = 1.37973  (rounded).\r\n" );
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document.write( "So, the exponential growth function is  \r\n" );
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document.write( "    B(t) = .\r\n" );
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document.write( "To answer first question, substitute t= 4 into the formula  B(4) =  = 1015 (rounded).\r\n" );
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document.write( "To answer the second question, solve an equation\r\n" );
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document.write( "    2630 = .\r\n" );
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document.write( "     = \r\n" );
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document.write( "    9.3929 = \r\n" );
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document.write( "    log(9.3929) = t*log(1.37973)\r\n" );
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document.write( "    t =  = 6.96 hours (about 7 hours).\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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\n" ); document.write( "\n" ); document.write( "To see many other similar and different solved problems on bacteria growth, look into the lesson\r
\n" ); document.write( "\n" ); document.write( " - Bacteria growth problems \r
\n" ); document.write( "\n" ); document.write( "in this site.\r
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\n" ); document.write( "\n" ); document.write( "Also, you have this free of charge online textbook in ALGEBRA-I in this site\r
\n" ); document.write( "\n" ); document.write( " - ALGEBRA-I - YOUR ONLINE TEXTBOOK.\r
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\n" ); document.write( "\n" ); document.write( "The referred lesson is the part of this online textbook under the topic \"Logarithms\".\r
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\n" ); document.write( "\n" ); document.write( "Save the link to this online textbook together with its description\r
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\n" ); document.write( "\n" ); document.write( "Free of charge online textbook in ALGEBRA-I
\n" ); document.write( "https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson\r
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\n" ); document.write( "\n" ); document.write( "to your archive and use it when it is needed.\r
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