a mining company extracts metal ore worth $a of revenue in year 0. its costs per year are $k, a constant. but the company expects its revenue to decline by p% each year. its mining activity will continue as long as the yearly revenue exceeds the yearly costs k.
(a) what is the revenue in year n? for how many years n* does the company operate?
(b) find the total profit in the period from year 0 to n*.
(c)put a=7, k=5, and p=2%. (i)what is n* in this case?
(ii) what is the associated total profit? (if you cannot solve (c)(i), pick arbitrarily n* = 14.)
hint: for any real number x is not equals to 1 and any ( finite) integer m, we have: m to the i=0 xi = (1- xm+1) / (1-x) .