If, under a given growth condition, the initial population of 104 CFU/mL of a bacterial species increases to 106 CFU/ in 120 minutes, what is the generation time?

To calculate the generation time, we use the formula derived from the exponential growth of bacteria:

\[
N_t = N_0 \times 2^{(t/T)}
\]

Where:
- \(N_t\) is the population at time \(t\) (106 CFU/mL),
- \(N_0\) is the initial population (104 CFU/mL),
- \(t\) is the time in minutes (120 minutes),
- \(T\) is the generation time (what we're trying to find).

To solve for \(T\), we first isolate \(2^{(t/T)}\) and take the logarithm:

\[
106 = 104 \times 2^{(120/T)}
\]
\[
\frac{106}{104} = 2^{(120/T)}
\]
\[
\log_2\left(\frac{106}{104}\right) = \frac{120}{T}
\]

Now, calculate \(\frac{106}{104}\), and solve for \(T\):

\[
\frac{106}{104} \approx 1.0192
\]
\[
\log_2(1.0192) \approx 0.0278
\]
\[
T = \frac{120}{0.0278} \approx 4317.27 \, \text{minutes}
\]

Thus, the generation time is approximately **43.17 minutes**.

Would you like further details on this, or do you have any questions?

Here are 5 related questions for further understanding:
1. How does environmental factors affect bacterial generation time?
2. What is the difference between CFU and OD measurements in microbiology?
3. How does generation time differ between various bacterial species?
4. What mathematical models are used for bacterial growth in different phases?
5. Can the same method be applied to calculate generation time for other organisms?

**Tip:** For faster-growing bacteria, factors like temperature, nutrients, and oxygen availability play critical roles in reducing the generation time.

If, under a given growth condition, the initial population of 104 CFU/mL of a bacterial species increases to 106 CFU/mL in 120 minutes, what is the generation time?

Learn how to calculate the generation time of bacteria given an initial population of 104 CFU/mL increasing to 106 CFU/mL in 120 minutes. This problem involves exponential growth concepts and logarithmic functions. Suitable for undergraduate biology and microbiology students.

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