1. The problem statement, all variables and given/known data We have the ODE y' = -ky + R for a population y(t) where death rate exceeds birth rate, counteracted by a constant restocking rate. I'm assuming k is the decay constant and R is the restocking rate The population at time t0 = 0 is y0, and I have to find a formula for y(t) Also, interpret the solution in terms of the long term behavior (0< y0 < R/k, y0 = R/k, and y0 > R/k). 2. Relevant equations y' = -ky + R 3. The attempt at a solution I solved the DE and got y = R/k + Ce^(-kt) But how do I know what this does in those given intervals of y0? Also if k = .5, R = 2, how would I graph the solutions?