A bacterial population increases from 100 to 100,000,000 in 15 hours. What is the generation time of this culture.
Answers
It should be B=b*2^n, so B/b=2^n=10^6
Take the log of both sides: 6= log2*n
log2=0.30103~=0.3, so n=20
then 20g=900, so g=~45 minutes.
hope it helps u
Answer: Generation time of the culture is 45 minutes.
Concept: Generation time = t/n
t = time
n = number of generations
Nt = N0(2^n)
Given: N0 = initial number of bacteria = 100
Nt = final number of bacteria = 100,000,000
To find: Generation time of the culture
Explanation:
N0 = initial number of bacteria = 100
Nt = final number of bacteria = 100,000,000
Generation time = t/n
t = time = 15 hours
n = number of generations
we have the time but we have to find number of generations.
We have the formula
Nt = N0(2^n)
putting values in the equation
100,000,000 = 1002^n
1000000 = 2^n
Taking log on both sides
n*log(2) = log1000000
log2 = 0.3
n = 6/0.3
n = 20
Generation time = t/n
Generation time = (15*60)/20
Generation time = 900/20
Generation time = 45 minutes.
Answer: Generation time of the culture is 45 minutes.
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