Question

Calculus help please!

Let C(t) be the number of cougars on an island at time t years (where t > 0). The number of cougars is increasing at a rate directly proportional to 3500 . C(t). Also, C(0) = 1000, and C(5) = 2000.

A. Find C(t) as a function of t only.
B. Calculate C(10).
C. Find the limit as t tends to infinity of C(t) , and explain its meaning.

Answer 1

for a, you just use the y-y1 = x-x1 slope formula right? because it's just linear

Answer 2

whats the rate of change

Answer 3

you can solve with graphing but it wont help you with calculus

Answer 4

I think it has to be a dy/dt kind of thing, rather than just linear or graphing :(

Answer 5

okay whats dy/dt then

Answer 6

dy/dt has to equal ky, but I don't know what k is

Answer 7

Oh wait no

Answer 8

dy/dt = 3500, integrate for y(t)

Answer 9

I think I have to use the P = M / (1 + A e^-kt) equation

Answer 10

ah I havnt done too many of those :/

Answer 11

I'm really not sure though... I mean M is the carrying capacity, but that's not given, so maybe that isn't the right equation, I don't know :(

Answer 12

http://openstudy.com/study#/updates/53572727e4b037e31a1a3a3e

Answer 13

https://answers.yahoo.com/question/index?qid=20090523114740AA2gNnX

Answer 14

see if that second one looks like your notes

Answer 15

The other openstudy question I'm having a little trouble following, but the yahoo one seems to match better!

Answer 16

I agree

Answer 17

B becomes easy enough to just plug 10 in, but C I don't know - there doesn't seem to be a limit, but they can't just continue to multiply with no end

Answer 18

Id just stick with the second link

Answer 19

The second link explains A perfectly, but doesn't address anything else unfortunately

Answer 20

@IDKwut you had posted about this problem, did you figure it out? I'm having trouble following your post