I need some help with the following problem:

My attempt

(a) I think to reach equilibrium it must satisfy

$\displaystyle \frac{dR}{dt} = 4000 \left( 1- \frac{4000}{130000} \right) - \alpha (4000)(160) = 0$

$\displaystyle \therefore \alpha = 6.05769 \times 10^{-3}$

Is this correct?

(b) When C=160 and R=4000, $\displaystyle \alpha RC = (6.05769 \times 10^{-3}) (4000)(160) = 3876.923$

So the contribution is that the population of the rabbits reduces by 3876.923 as the result of the interaction?

Could anyone show me how we can calculate how many rabbits did each cat eliminate per year? Any help would be greatly appreciated.