The question is: 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.
I started with $dC/dt = 3500C$. Solving that gives $C = Ae^{3500t}$. Is this all wrong?
There's another part: c. Find the limit as $t$ tends to infinity of $C(t)$ , and explain its meaning.
any help would, well, help! thank you!
You are almost right. You should start with
$$\frac{dC}{dt}=3500kC$$
since it says "directly proportional to". Then your answer should contain this $k$ and the other constant $A$ which is the initial condition. Then use the other given condition, you can find $k$.
Use this equation, you can find the limit when $t\rightarrow \infty$.