SOLUTION: 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

Question 212974This question is from textbook Elementary and Intermediate Algebra
: 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? This question is from textbook Elementary and Intermediate Algebra

Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!
Starting with 25,000 bacteria present at time zero, you can write:
Note: The exponent is really =
At what time,t, will the bacteria count reach 100,000,000? Set N(t) = 100,000,000 and solve for t.
Divide both sides by 25000.
Take the logarithm of both sides.
Apply the power rule for logarithms.
Divide both sides by
Multiply both sides by 20.
Evaluate.
Minutes. Round up to:
Minutes. Convert to hours.
hours. Add this to 11:00am to get 15:00 hours. Subtract 12 hours.
Time = 3:00pm
Infection can occur at 3:00pm
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