Logistic differential problem

In summary, the logistic differential problem is a mathematical model used to describe the growth of a population over time. It takes into account limiting factors and can be solved using various mathematical techniques or computer algorithms. The carrying capacity is a crucial component in this problem, representing the maximum sustainable population size. Real-world applications include predicting population growth, understanding infectious diseases, and optimizing resource management. However, there are limitations to this model, such as assuming a constant carrying capacity and not accounting for external factors or sudden changes in population size.
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goomer
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1. A population, P(t), satisfies the logistic differential equation dP/dt = (2/3)P(5-P/100). What is lim as t --> infinity P(t)?

I know you're supposed to factor out the 5 to get dP/dt = (10/3)P(1-P/20)

Any ideas?

2. M/(1+Ae^-kt) where A = (M-Po)/Po



3. I'm know k = 10/3 and M = 20
I'm trying to plug everything into
I think Po is initial population, but don't know where to go from there
 
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Sorry for the repeat portion
 

1. What is the logistic differential problem?

The logistic differential problem is a mathematical model that describes the growth of a population over time, taking into account limiting factors such as resource availability and carrying capacity. It is a type of differential equation that is commonly used in population biology and ecology.

2. How is the logistic differential problem solved?

The logistic differential problem can be solved using various mathematical techniques, such as separation of variables, substitution, or using an integrating factor. However, it can also be solved numerically using computer algorithms.

3. What is the significance of the carrying capacity in the logistic differential problem?

The carrying capacity, also known as the maximum sustainable population size, is a crucial component in the logistic differential problem. It represents the maximum number of individuals that can be supported by the available resources in a given environment. As the population approaches the carrying capacity, the growth rate slows down and eventually reaches a stable equilibrium.

4. What are the real-world applications of the logistic differential problem?

The logistic differential problem has many practical applications, including predicting population growth in biology and ecology, understanding the dynamics of infectious diseases, and optimizing resource management in economics and business. It is also used in fields such as demography, epidemiology, and sustainability studies.

5. Are there any limitations to the logistic differential problem?

Like any mathematical model, the logistic differential problem has its limitations. It assumes a constant carrying capacity, which may not always be realistic in certain situations. It also does not account for external factors, such as natural disasters or human intervention, that can impact population growth. Additionally, the model may not accurately predict sudden changes or fluctuations in population size.

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