Luria-delbruck experiment question

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My question is about the classic study cited below (*) and available as a free pdf download from

At page 495 the authors use the "average division time" of bacteria dt, divided by ln(2), as the time unit in the equations

(1) dN_t /dt = N_t , (2) N_t = N_o e^t.

Can anyone tell me why this division by ln(2) was done? N_o is the original number of bacteria present. N_t is the number at time t.

Obviously it has something to do with integration/differentiation, but I am missing the point. Thanks.

*Luria, S. E.; Delbrück, M. (1943). "Mutations of Bacteria from Virus Sensitivity to Virus Resistance". Genetics 28 (6): 491–511.

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  • #2
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The doubling time divided by ln(2) gives the appropriate time constant for an exponential growth. Writing the equation for exponential growth in terms of the doubling time (td) gives:

N(t) = No 2^(t/td)

Equivalently, this can be written as:

N(t) = No e^(t ln(2) / td) = No e^(t/tc)

Where tc = td/ln(2). This makes use of the fact that e^ln(2) = 2.
  • #3
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Bacteria double exponentially; 2 become 4, 4 become 8, etc. This describes Log in base 2 (22, 23, etc).

The application then is used to describe things that grow or decay exponentially. A more detailed explanation can be found" [Broken]
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  • #4
N(t) = No 2^(t/td)

Equivalently, this can be written as:

N(t) = No e^(t ln(2) / td) ...
This is crystal clear. I forgot he was starting with 2^t/td as a growth law. Thanks!