Question

Let P(t) represent the number of wolves in a pop. at time t in years, when t is greater than or equal to 0. The pop. P(t) is increasing at a rate directly proportional to 800-P(t), where the constant of proportionality is k.

I just want to know if my setting up of the equation is correct.
800-P(t)=Ae^(kt).

Answer 1

You are probably a little ahead of the game. What you have proposed on the right hand side has something to do with the solution of the differential equation that you are attempting to set-up.

The problem statement is:
P(t)=number of wolves, P≥0
t=time in years
P(t) is increasing at a rate of k(800-P(t)), which means
d(P(t))/dt = k*(800-P(t)) ... (1)
where k>0
The solution of (1) will give an expression related to the right-hand side of your equation.