Growth of bacteria diff. eq help

In summary, differential equations are mathematical equations that describe the relationship between a function and its derivatives. In the context of bacteria growth, they can be used to model the rate of change of the number of bacteria over time. The initial conditions for a bacteria growth differential equation can be determined by collecting data on the initial population and growth rate. These equations can be used to predict future populations, but their accuracy may vary based on initial conditions and assumptions. External factors like temperature and nutrient availability can be incorporated into the equation to make it more accurate. However, there are limitations to using differential equations to model bacteria growth, such as the assumption of constant growth rate and the exclusion of other factors that may affect growth.
  • #1
mayeh
15
0
a bacterial population B is known to have a rate of growth proportional to B itself. if between noon and 2 PM the population triples, at what time, no controls exerted should B become 100 times what it was at noon?


what does it mean by between noon and 2pm? does it mean that it takes 2hrs for the bacteria to triple? or the bacteria triples from 12 to the middle of 12 and 2?
 
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  • #2
F(1400 hours) = 3 x F(noon).
 
  • #3
sorry, i don't get it...

could you please explain further.
 
Last edited:
  • #4
Population at 1400 hours (2 PM) = 3 times the population at noon.
 

1. What is a differential equation and how is it related to the growth of bacteria?

A differential equation is a mathematical equation that describes the relationship between a function and its derivatives. In the context of bacteria growth, a differential equation can be used to model the rate of change of the number of bacteria over time.

2. How do you determine the initial conditions for a bacteria growth differential equation?

The initial conditions for a bacteria growth differential equation can be determined by collecting data on the initial population of bacteria and their growth rate. This data can be used to determine the initial number of bacteria and their initial growth rate, which are necessary parameters for the differential equation.

3. Can bacteria growth differential equations be used to predict future populations?

Yes, bacteria growth differential equations can be used to predict future populations by solving the equation for different time points. However, the accuracy of the predictions may vary depending on the accuracy of the initial conditions and the assumptions made in the equation.

4. How do external factors, such as temperature and nutrient availability, affect the growth of bacteria described by a differential equation?

External factors like temperature and nutrient availability can be incorporated into the differential equation by adding additional terms that account for their influence on the growth rate of bacteria. This can make the model more accurate and representative of real-life conditions.

5. What are some limitations of using differential equations to model bacteria growth?

Some limitations of using differential equations to model bacteria growth include the assumption of constant growth rate, which may not always hold true in real-life situations. Additionally, the accuracy of the model may be affected by the quality of the initial conditions and the assumptions made in the equation. Other factors, such as competition with other organisms, may also affect the growth of bacteria and are not accounted for in simple differential equations.

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