Math Help - Calculur problem help please

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.

2. Re: Calculur problem help please

Originally Posted by munkhuu
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.
a) Correct
b) Correct, but you typed in the wrong expression for the derivative (you probably have the right one)
c) The differential of N is $\Delta N = N(t+1) - N(t) = \frac{n(s+1)}{t + 1} - \frac{ns}{t} = \ldots$
d) Just like c) except now the second sample tagged number remains the same, whilst s increases by one.

3. Re: Calculur problem help please

Hey. I just ask one more thing bout different topic. How do u find direction if gradient is given. For example gradient is <12,20,30> and i need to find which directoo. Its going do i find the unit vector or smthn?

4. Re: Calculur problem help please

Well, gradient is a direction and magnitude, a vector specifically, so your question is too vague stated in this way. A unit vector would give the direction as well as the original vector.

P.S. it's a bit rude not to be appreciate for the previous help if you're going to ask another question, and it would be best if you expressed this before moving on so abruptly. Just my opinion.

5. Re: Calculur problem help please

Im sorry good sir. I apologize. Thank you very much. I was i a hurry.
The second question states that there is function f(x y z) and point (x.y.z) and gradient is (20.30.15) and which dorection should i go to reach the point. I was little confused

6. Re: Calculur problem help please

To find a unit vector in the direction of a given vector, find the length of the vector and divide by it.