If the doubling time of a bacterial population is 3 hours, then its average specific growth rate during this period is _________ $h^{-1}$. (Round off to two decimal places)
Understanding Bacterial Growth Rate
The question asks for the average specific growth rate ($\mu_{avg}$) of a bacterial population given its doubling time ($t_d$). The doubling time is the time it takes for the population to double in size.
Calculating Specific Growth Rate
The relationship between the average specific growth rate and doubling time is defined by the formula:
$ \mu_{avg} = \frac{\ln(2)}{t_d} $
Where:
- $\mu_{avg}$ is the average specific growth rate (in $h^{-1}$)
- $\ln(2)$ is the natural logarithm of 2 (approximately 0.693)
- $t_d$ is the doubling time (in hours)
Applying the Formula
Given the doubling time $t_d = 3$ hours:
- Substitute the values into the formula:
$ \mu_{avg} = \frac{\ln(2)}{3 \text{ h}} $
- Calculate the value:
$ \mu_{avg} \approx \frac{0.693147}{3 \text{ h}} \approx 0.231049 \text{ h}^{-1} $
- Round the result to two decimal places as requested:
$ \mu_{avg} \approx 0.23 \text{ h}^{-1} $
The calculated average specific growth rate is approximately 0.23 $h^{-1}$. This value falls within the range of 0.2 to 0.25.
Important Questions from Kinetics of Cell Growth Substrate Utilization and Product Formation
If the rate at which $E. coli$ divides is $0.5 \text{ h}^{-1}$, then its doubling time is _______________ h.
- Which of the following factors can affect the growth of a microbial culture in a batch cultivation process?
Let $y(t)$ be a bacterial population whose growth is given by
$ \frac{dy}{dt} = \lambda(y + 2) $
where $ \lambda $ is the growth rate constant. If $y(0) = 1$ and $y(1) = 4$, then the value of $ \lambda $ is
- A microorganism is grown in a batch culture using glucose as a carbon source. The apparent growth yield is $0.5 \frac{\text{g biomass}}{\text{g substrate}}$. The initial concentrations of biomass and substrate are $2 \text{ g L}^{-1}$ and $200 \text{ g L}^{-1}$, respectively. Assuming that there is no endogenous metabolism, the maximum biomass concentration that can be achieved is ________ $\text{g L}^{-1}$.
- Which one of the following represents non-growth associated product formation kinetics in a bioprocess system? X and P denote viable cell and product concentrations, respectively.
