document.write( "Question 212974This question is from textbook Elementary and Intermediate Algebra
\n" ); document.write( ": Growth of bacteria. The bacteria Escherichia coli (E. coli) are commonly found in the human bladder. Suppose that 3000 of the bacteria are present at time t=0. Then t minutes later, the number of bacteria present is N(t) = 3000(2)^t/20. if 100,000,000 bacteria accumulate, a bladder infection can occur. If, at 11:00am, a patient's bladder contains 25,000 E. coli bacteria, at what time can infection occur? \n" ); document.write( "

Algebra.Com's Answer #160926 by Earlsdon(6294) $\"\"$ $\"About$

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Starting with 25,000 bacteria present at time zero, you can write:
\n" ); document.write( " $\"N%28t%29+=+25000%282%29%5E%28t%2F20%29\"$ Note: The exponent is really = $\"t%2F20\"$
\n" ); document.write( "At what time,t, will the bacteria count reach 100,000,000? Set N(t) = 100,000,000 and solve for t.
\n" ); document.write( " $\"100000000+=+25000%282%29%5E%28t%2F20%29\"$ Divide both sides by 25000.
\n" ); document.write( " $\"4000+=+%282%29%5E%28t%2F20%29\"$ Take the logarithm of both sides.
\n" ); document.write( " $\"log%28%284000%29%29+=+log%28%282%29%29%5E%28t%2F20%29\"$ Apply the power rule for logarithms.
\n" ); document.write( " $\"log%28%284000%29%29+=+%28t%2F20%29log%28%282%29%29\"$ Divide both sides by $\"log%28%282%29%29\"$
\n" ); document.write( " $\"t%2F20+=+log%28%284000%29%29%2Flog%28%282%29%29\"$ Multiply both sides by 20.
\n" ); document.write( " $\"t+=+20%2Alog%28%284000%29%29%2Flog%28%282%29%29\"$ Evaluate.
\n" ); document.write( " $\"t+=+239.3156\"$ Minutes. Round up to:
\n" ); document.write( " $\"t+=+240\"$ Minutes. Convert to hours. $\"240%2F60+=+4\"$
\n" ); document.write( " $\"t+=+4\"$ hours. Add this to 11:00am to get 15:00 hours. Subtract 12 hours.
\n" ); document.write( "Time = 3:00pm
\n" ); document.write( "Infection can occur at 3:00pm \n" ); document.write( "

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