document.write( "Question 131525: Hello the chapter im working on is called exponential and logarithmic functions. The section is on exploring exponential models. Could you help me with this exponential growth word problem on bacteria?\r
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\n" ); document.write( "\n" ); document.write( "A scientist notes the bacteria count in a petrie dish is 50. Two hours later, he notes the count has increased to 80. If this rate of growth continues, how much more time will it take for the bacteria count to reach 100?\r
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Algebra.Com's Answer #96004 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
Hello the chapter im working on is called exponential and logarithmic functions. The section is on exploring exponential models. Could you help me with this exponential growth word problem on bacteria?
\n" ); document.write( "Here it is:
\n" ); document.write( "A scientist notes the bacteria count in a petrie dish is 50. Two hours later, he notes the count has increased to 80. If this rate of growth continues, how much more time will it take for the bacteria count to reach 100?
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document.write( "The formula spells the word \"Pert\"\r\n" );
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document.write( "A = Pert\r\n" );
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document.write( "At time t = 0, the amount of bacteria in the dish, A, is 50.\r\n" );
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document.write( "Substituting:\r\n" );
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document.write( "50 = Pert\r\n" );
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document.write( "50 = Per(0)\r\n" );
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document.write( "50 = Pe0\r\n" );
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document.write( "50 = P(1)\r\n" );
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document.write( "50 = P\r\n" );
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document.write( "So the formula A = Pert\r\n" );
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document.write( "is now\r\n" );
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document.write( "A = 50ert\r\n" );
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document.write( ">>...Two hours later, he notes the count has increased to 80...<< \r\n" );
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document.write( "Therefore, at time t = 2, the amount of bacteria in the dish, A, is 80.\r\n" );
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document.write( "Substituting:\r\n" );
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document.write( "80 = 50ert\r\n" );
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document.write( "80 = 50er(2)\r\n" );
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document.write( "80 = 50e2r\r\n" );
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document.write( "Divide both sides by 50\r\n" );
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document.write( "\"80%2F50\" = e2r\r\n" );
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document.write( "1.6 = e2r\r\n" );
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document.write( "Use the definition formula for\r\n" );
document.write( "a natural logarithm:\r\n" );
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document.write( "M = eN  is equivalent to ln(M) = N\r\n" );
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document.write( "So\r\n" );
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document.write( "1.6 = e2r \r\n" );
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document.write( "becomes\r\n" );
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document.write( "ln(1.6) = 2r\r\n" );
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document.write( "Use a calculator to find ln(1.6) = 0.4700036292,\r\n" );
document.write( "rounding to 0.470\r\n" );
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document.write( "0.470 = 2r\r\n" );
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document.write( "Divide both sides by 2\r\n" );
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document.write( "0.235 = r\r\n" );
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document.write( "Now the formula\r\n" );
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document.write( "A = 50ert\r\n" );
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document.write( "becomes\r\n" );
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document.write( "A = 50e0.235t\r\n" );
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document.write( "Now the question is:\r\n" );
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document.write( ">>...how much more time will it take for\r\n" );
document.write( "     the bacteria count to reach 100?...<<\r\n" );
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document.write( "We substitute 100 for A and solve for t\r\n" );
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document.write( "100 = 50e0.235t\r\n" );
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document.write( "Divide both sides by 50\r\n" );
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document.write( "\"100%2F50\" = e0.235t\r\n" );
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document.write( "2 = e0.235t\r\n" );
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document.write( "Use the definition formula again for\r\n" );
document.write( "a natural logarithm:\r\n" );
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document.write( "M = eN  is equivalent to ln(M) = N\r\n" );
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document.write( "So\r\n" );
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document.write( "ln(2) = 0.235t\r\n" );
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document.write( "Get ln(2) from calculator as 0.6931471806, rounding\r\n" );
document.write( "to 0.693\r\n" );
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document.write( "0.693 = 0.235t\r\n" );
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document.write( "Divide both sides by 0.235\r\n" );
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document.write( "\"0.693%2F0.235\" = t\r\n" );
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document.write( "2.95 = t\r\n" );
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document.write( "Multiplying 60 minutes times the decimal\r\n" );
document.write( "part, .95, gives 57 minutes, so\r\n" );
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document.write( "It takes about 2 hours and 57 minutes.\r\n" );
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document.write( "However since the question asks \"how much MORE time\",\r\n" );
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document.write( "the answer is 57 minutes. \r\n" );
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document.write( "Edwin
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