The following example of another experiment might help you check your math. Supp

Question

The following example of another experiment might help you check your math. Suppose 3 times 10^4 bacteria were inoculated into a culture and incubated for 24 hours. After incubation, the number of cells was determined to be 6 times 10^7 cells. Calculate the growth rate and the doubling time. # doublings = log_10 [6 times 10^7] = log_10 [3 times 10^4]/log_10 2 = 7.778 - 4.477/0.301 = 3.301/0.301 = 10.967 doublings growth rate = # doublings/time = 10.967 doublings/24 hours = 0.457 doublings/hour = 0.457 generations/hour doubling time = 1/growth rate - 1/0.457 = 2.19 hours/generation

Explanation / Answer

Initial bacterial count = 3 x 10 4

Final bacterial count = 6 x 10 7

Duration = 24 hours

Number of generations present is given by the formula,

(log (final count) - log (initial count)) / log 2

= (log(6 x 10 7) - log (3 x 10 4)) / log 2

= (7.778-4.477)/0.301

= 3.301/0.301

= 10.967 generations

There are 10.967 generations in 24 hours

Therefore, the growth rate is,

= 10.967/24

= 0.457/hour

The time taken to complete one generation is given by the formula,

= 1/growth rate

= 1/0.457

= 2.19 hours for one generation

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