Remove grain before growth and retain the exact supply bound

A grain facility holds $10000$ bushels at the end of December 2013. Insurance pay-outs purchase extra grain, increasing the stock by $2\%$ before the end of every month.

(a) Find the stock at the end of December 2014.1 mark

(b) During January–December 2014 the facility supplies x bushels to a laboratory each month, before the $2\%$ addition.

(i) For $x=100$, show the end-March stock is $10299.9$ bushels to 1 d.p.2 marks

(ii) Find the maximum monthly supply.4 marks