Unfold a loss-then-top-up recurrence in two directions

A storage tank loses $10\%$ of its water each day, then receives $90$ litres at the end of the day. Let $x_n$ be the volume after n days and $x_0$ its initial volume.

(i) Give a recurrence.1 mark

(ii) Show $x_n=0.9^n(x_0-900)+900$.3 marks

(iii) Deduce the limiting volume.1 mark