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.