75000 live bacteria present in a culture in a flask. When antibiotic is added to the culture, the number of live bacteria is reduced by half every four hours. Approximately how many hours have passed when there are 1500 bacteria left alive?

A. 22.3 hours
B. 22.6 hours
C. 22.9 hours
D. 22.2 hours

2 Answer

  • The number of bacteria at any time t where t is number of hours is given by the equation,
                                    At = Ao(1/2)^t/4
    where Ao is the original number of bacteria. Substituting the known values from the equation,
                                    1500 = (75000)(0.5)^t/4
    The value of t from the equation is equal to 22.57 hours. 
  • Answer: 22.6

    Step-by-step explanation: