A person's capital at the beginning of, and expenditure during, a given year k are denoted by Ck and Ek respectively, and satisfy the difference equations
(a) Show that eventually the person's capital grows at 20% per annum.
(b) If the capital at the beginning of year 1 is £6000 and the expenditure during year 1 is £3720 then find the year in which the expenditure is a minimum and the capital at the beginning of that year.