k = 0.1;
m0 = 2;
y0 = 1;
soln = 
      DSolve[{-y'[t] == k*y[t]*(m0 - y[t]), 
          y[0] == y0}, y[t], t]

sol = soln[[1, 1, 2]]
rate = k*sol*(m0 - sol)

Plot[rate, {t, 0, 10}];