Question

75,000 live bacteria are present in a culture in a flask. When an 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 2000 bacteria left alive?

Answer 1

Model:

number of hours            number of bacteria

0                                      75000

4*1                                      75000 / (2^1)

4*2                                      75000 / (2^2)

4*3                                      75000 / (2^3)

4*4                                      75000 / (2^4)


4*n                                      75000 / (2^n)


=> 2000 = 75000 / (2^n)


=> 2^n = 75000 /2000


= 2^n = 37.5


=> n log(2) = log (37.5)

=> n = log (37.5) / log (2)


=> n =   5,2288


=> 4*n = 20.91


Answer: approximately 21 hours.