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## Homework Statement

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).

## Homework Equations

y' = -ky + R

## 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?