Compare a geometric training total with an arithmetic total

(i) Swimmer A swims $50$ m on day one and increases each subsequent day’s distance by $10\%$ of the previous day’s distance for $30$ days.

(a) Show her day-30 distance is $793$ m to the nearest metre.2 marks

(b) Find her total in 30 days to the nearest metre.2 marks

(ii) Swimmer B starts at $50$ m and adds $5$ m each day. Find the least number of days for B’s total to exceed A’s total in (i)(b).5 marks