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Math Help - birth rate DE problem

  1. #1
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    birth rate DE problem

    Dear Sir
    I would be grateful if you can help me to solve the the below questions
    The answers are: a)31.54 million b) 13.44 million c)1179 million

    thanks
    Kingsman
    Attached Thumbnails Attached Thumbnails birth rate DE problem-india.jpg  
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  2. #2
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    So, according to the problem statement, what DE could you write down, do you think?
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  3. #3
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    a) db/dt=0.0428b with when t=o,b=0
    b) db/dt=-0.0167b with t=o b=o
    c) db/dt=(0.0428-0.0167)b with when t=0.b=598100000
    thanks
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  4. #4
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    Dear Adrian C. Keister
    Thanks for the response and below is my working but I fail to find out where is my mistake; i just cannot get the answer.
    Please help!
    thanks

    a) db/dt=0.0428b with when t=o,b=0
    b) db/dt=-0.0167b with t=o b=o
    c) db/dt=(0.0428-0.0167)b with when t=0.b=598100000
    Kingsman
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  5. #5
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    I would use the population as the independent variable here. On the LHS, you should have the rate of change. On the RHS, you should have all the terms that affect the population's rate of change. What are those?
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  6. #6
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    Thanks Adrian C. Keister for the response but I WONDER where did I go wrong in my DE and incidentally in db/dt=0.0428b when=o,b=0, "b' stands for number of birth.I would appreciate very much if you show me how the correct DE looks like.
    Thanks
    kingsman
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  7. #7
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    As I said, you should write your DE with population as the dependent variable, not births or deaths. The reason is that population will reflect both births and deaths, whereas births or deaths by themselves will not reflect the other. Here is my thought on the DE:

    \displaystyle \frac{dP}{dt}=0.0428P-0.0167P=0.0261P, subject to P(0)=5.981\times 10^{8}. Here we have assumed that t=0 corresponds to the year 1974.

    Now, what is the solution of this DE?
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  8. #8
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    Dear Adrian C. Keister,
    Thanks very much but your DE which gives answer to part a which I think should be the DE for part C question. How about the DE for the other 2 parts.: I am still struggling with it-Please Help!
    Thanks very much
    Kingsman
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  9. #9
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    The issue is that both the birth rate and the death rate depend on the current population, according to the problem statement. And, of course, the population depends on the birth rate and the death rate. Therefore, in order to answer all your questions, you're simply going to have to find the population (the linking variable here) for all time, and then you can multiply by the indicated percentages to find the birth rate and the death rate in the indicated years.

    Does that make more sense?
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  10. #10
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    Dear Adrian C. Keister,
    Thanks very much but I only manage to get the answer to part c leaving part b and a hanging in the
    air without knowing where did I go wrong.I would appreciate very much if someone can show me the DE for part a and b

    Thanks very much
    Kingsman
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  11. #11
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    The DE is the same for all three parts. Show your work, and I might be able to see what you're doing wrong (if anything).
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