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Calculus problem about population count

  1. Mar 18, 2013 #1
    1. The problem statement, all variables and given/known data
    Calculus question about tag and recapture?
    Here is the problem, i tried to do most of it but don't understand what its asking on c and d.
    Tag and recapture is used to estimate populations of animals in the wild. First, sample of animals are captured, number=n. They are tagged and released back into the wild. Sometime later, another sample of animals are captured, number=s. Of the s animals in the second sample t are found to be tagged. The estimate of total animal N is ofund from N/n=s/t.
    Supposed n=100, s=60, t=15. In the second sample 1/4 of the animals were tagged.
    a) what is the total animal population based on these results.
    i got 400
    b) what is dN/dt of n=100 s=60 t=15
    i got -26.67 idk what the negative is saying. i said N=ns/t and dN/dt= -st/t^2 i hope its right.
    c) what is the differential change in N if one more animal had been captured in the second sample and it was found to be tagged. express your answer in whole animals. I dont really understand the equation so i dont know what to do.
    i just substitued the 100 for n and 61 for s and 16 for t for the dN/dt= -st/t^2 equation and got -23.83
    d) what is the the differential change in N if one more animal had been captured in the second sample and it was not found to be tagged. This is almost the same as c so i dont know.
    Please help me atleast understand what c and d is asking. and how to start it.
     
  2. jcsd
  3. Mar 18, 2013 #2

    HallsofIvy

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    Yes, that is correct.

    You mean, I think, dN/dt= -sn/t^2. Now, evaluate that at n=100, s= 60, t= 15.

    "s" was the number of animals in the second saple and t was the number tagged.
    "if one more animal had been captured in the second sample and it was found to be tagged"
    So replace s with s+ 1 and t with t+ 1. That is, s= 61 and t= 16, just as you say.

    Yes, it is the same. Now s= s+1= 61 but t remains 15.

     
  4. Mar 18, 2013 #3
    thank you very much, but just few questions. Why is the answer for c and d are negative? and when it says express your answer in whole animals, i subtract 23.83 from 26.67 and get 2.84. Is the answer 2 or 3?
     
  5. Mar 18, 2013 #4

    HallsofIvy

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    (c) and (d) ask for derivatives- the rate at which the populations are changing. If those derivatives are negative, it means the populations are declining. "2.84" is closer to 2 than to three so would be rounded up to 3.
     
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