Continuous Growth
Continuous Growth - Related Videos
01:22
Continuous Culture of Bacteria at Constant Density via Automated Growth Rate Estimation
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2025
Begin with a turbidostat, a device that maintains a constant cell density in culture.The device contains a vessel with a bacterial culture, which is continuously aerated by stirring and maintained at a constant temperature.A laser diode emits a light beam that is split into two paths.One path is directed to a reference sensor to monitor laser intensity fluctuations, while the other passes through the culture.Bacterial cells scatter and absorb light, decreasing the transmitted intensity, which...
07:26
Designing Automated, High-throughput, Continuous Cell Growth Experiments Using eVOLVER
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Cited by 22 •
2019
The eVOLVER framework enables high-throughput continuous microbial culture with high resolution and dynamic control over experimental parameters. This protocol demonstrates how to apply the system to conduct a complex fitness experiment, guiding users on programming automated control over many individual cultures, measuring, collecting, and interacting with experimental data in real-time.
09:40
Batch and Continuous Bioreactors
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2023
Bioreactors are used to grow organisms in large volumes, thereby enabling the production of mass quantities of the target product. These reactors can be batch reactors, which contain all of the components needed for cell growth, or continuous reactors, which have inlet and outlet ports allowing for the addition of fresh growth media and the removal of cell waste. This video presents batch and continuous reactors and demonstrates the use of bioreactors to grow bacteria in the laboratory.
04:45
Population Growth - Concepts
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2019
Population Models An ecological population is a group of individuals of a single species living in an area at the same time. To persist, a population must either grow or maintain its size. Population ecology is the study of how population size and age distribution change over time through interactions with other species and the environment as well as with individuals of their own species. A particularly important feature that is studied by ecologists is the rate at which a population grows or...
14:47
Population Growth - Student Protocol
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2019
Exponential Population Growth Model ExpandNOTE: In these experiments you will use computer software to simulate different types of growth models. HYPOTHESES: The experimental hypothesis might be that if we increase either R, the reproductive rate or the initial population size, NT, that this will increase the population size after 10 generations in an exponential growth model compared to unmanipulated control populations. The null hypothesis may be that populations of different R and initial...
FAQs
The parameter k sets the proportionality between a quantity's current size and its rate of change. When k is positive, the model produces exponential increase; when k is negative, it produces continuous decay. Thus, examining the sign of k identifies whether the modeled quantity rises or falls, while its value specifies the rate relationship.
The natural exponential function appears because it supplies the solution form that remains consistent with the differential equation dA/dt = kA. Writing the result as A(t) = A₀e^{kt} connects the model's instantaneous rate rule to a usable expression for the quantity at time t. This link is central to how differential equations represent smooth change in mathematics.
Unlike a model that updates a quantity at separate time points, continuous growth represents change as occurring at every instant. This distinction matters because the differential equation describes an ongoing rate, while the solution gives the amount at any selected time. The approach is therefore suited to systems whose changes are modeled as smooth rather than as a sequence of isolated updates.
Begin with the initial amount A₀, identify the proportionality constant k, and specify the time t. Substitute these quantities into A(t) = A₀e^{kt}; the resulting value gives the modeled amount at that time. Interpreting k's sign then indicates whether the calculation represents exponential increase or continuous decay. This workflow translates the differential equation into a direct evaluation.
When interest is compounded continuously, the model treats the account balance as changing smoothly rather than at separated compounding times. The initial balance serves as A₀, the relevant growth constant as k, and elapsed time as t. Evaluating A₀e^{kt} then gives the modeled balance for the selected time, making the method useful for analyzing continuously compounded financial growth.
These applications can be represented within one mathematical framework even though their practical meanings differ. In a population model, the quantity may describe a changing population; in radioactive decay, it describes a quantity decreasing over time. The sign of k helps distinguish increase from decay, while A₀ and t identify the starting amount and time under study.