Assume that in the absence of immigration and emigration, the growth of a country's population P(t) satisfies dP/dt = kP for some constant k > 0 (see Equation (1) of Section 1.3). Determine a differential equation governing the growing population P(t) of the country when individuals are allowed to immigrate into the country at a constant rate r > 0. (Use P for P(t).) dP dt = What is the differential equation for the population P(t) of the country when individuals are allowed to emigrate at a constant rate r > 0? dP dt =

Answers 2

Answer:

A) Differential equation for population growth in case of individual immigration is:

\frac{dP}{dt}=kP+r

B) Differential equation for population growth in case of individual emigration is:

\frac{dP}{dt}=kP-r

Step-by-step explanation:

Population growth rate  in the absence of immigration and emigration is given as:

\frac{dP}{dt}=kP--(1)

A) When individuals are allowed to immigrate:

Let r be the constant rate of individual immigration given that r >0.

Differential equation for population growth in this case is:

\frac{dP}{dt}=kP+r

B) In case of individual emigration:

Let r be the constant rate of individual emigration given that r >0.

Differential equation for population growth in this case is:

\frac{dP}{dt}=kP-r

AI generated Answer

. The differential equation governing the population P(t) of the country when individuals are allowed to immigrate into the country at a constant rate r > 0 is: dP/dt = kP + r. The differential equation for the population P(t) of the country when individuals are allowed to emigrate at a constant rate r> 0 is: dP/dt = kP - r. This equation represents the rate of change of the population, taking into account both the natural growth rate and the emigration rate. Note that if the emigration rate is greater than the natural growth rate (r > k), then the population will decrease over time.
  • Rate an answer:

Do you know an answer? Add it here!

Can't find the answer?

Unable to find an answer to your question?

Don't worry! There are several alternative approaches you can try to resolve your query. Here are some tips to help you find answers in different ways:

  1. Reframe your question: Sometimes, the way you phrase your question can limit your search results. Try rephrasing it using different keywords or providing more context to get better results.
  2. Utilize social media: Post your question on social media platforms, particularly those focused on professional or specialized topics. Twitter, LinkedIn, and Facebook groups can connect you with individuals who may have relevant expertise or experiences to share.
  3. Consult subject matter experts: Reach out to experts in the field related to your question. Many professionals are willing to help and share their knowledge. You can connect with them through email, LinkedIn messages, or by attending relevant conferences or events.
  4. Use our website to find your question through the search box above, or you can sign up to ask your question for our big educational community. Our experts will review your question, and you will get a quick and quality answer.
  5. Collaborate with others: If your question is related to a specific project or problem, consider collaborating with others who might have complementary skills or knowledge. Teamwork can lead to innovative solutions and shared insights.

Remember, the process of finding answers often involves persistence, creativity, and an open mind. By exploring various resources, reaching out to others, and being proactive in your search, you increase your chances of finding the information you need. Happy quest for knowledge!

Login with Google

or

Forgot your password?

I don't have an account, I want to Register

Choose a language and a region
How much to ban the user?
1 hour 1 day 100 years