If a bacterial culture has a doubling time of 50 minutes then what wil...
As specific growth is equal to ln 2/ Doubling time
Specific growth (µ) = 0.693/50
= 0.0138min–1
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If a bacterial culture has a doubling time of 50 minutes then what wil...
The specific growth rate of a bacterial culture can be calculated using the formula:
Specific Growth Rate (μ) = ln(Nf/Ni) / Δt
Where:
μ = specific growth rate
Nf = final population size
Ni = initial population size
Δt = time interval
In this case, the doubling time is given as 50 minutes. The doubling time is the time it takes for the population to double in size.
To calculate the specific growth rate, we need to find the natural logarithm of the ratio of the final population size to the initial population size, divided by the doubling time.
Let's assume the initial population size is 1. This means that after 50 minutes, the population will double to 2. Therefore, Nf/Ni = 2/1 = 2.
Using the formula, we can calculate the specific growth rate:
μ = ln(2) / 50
Calculating the natural logarithm of 2 gives approximately 0.693:
μ = 0.693 / 50
Simplifying this equation gives:
μ = 0.01386 min^-1
So, the specific growth rate of the bacterial culture is approximately 0.0138 min^-1, which corresponds to option B.
To summarize:
- Doubling time is the time it takes for the population to double in size.
- Specific growth rate is calculated using the formula μ = ln(Nf/Ni) / Δt.
- In this case, the doubling time is 50 minutes.
- Assuming the initial population size is 1, the final population size after 50 minutes will be 2.
- Using the formula, we find that the specific growth rate is approximately 0.0138 min^-1, which corresponds to option B.