An iron mining company depletes 1/11 of the iron ore in a pit it mines over a year. If the company opens a new iron ore mining pit in year 1 and if the initial reserves of the pit were estimated to be 9000 MT (million tons), what is the approximate total quantity of iron ore that would have been mined from that pit by the end of year 4?
Choose the correct choice from the following options.
A) 5728 MT  B) 2853 MT  C) 4514 MT  D) 3152 MT  E) 1510 MT
X is the initial quantity of the iron ore in the pit.   After a year of mining the quantity of iron ore left would be X1=X-1/11X i.e. X1=10/11X   Same thing for X2, X3, X4, respectively representing the quantity left after 2, 3, 4 years of mining. (quantity at the end of the year)   So we have:   X1=10/11 X   X2=10/11 X1   X3=10/11 X2   X4=10/11 X3   By multiplying both ends of the equations we get:   X1*X2*X3*X4 = (10/11)^4 X*X1*X2*X3   Simplification leaves us with:   X4 = (10/11)^4 X   X4 is the quantity left at the pit by the end of year4. So the cumulative quantity (Q4) that has been mined from the pit after 4 years is: Q4= X-X4=X-(10/11)^4X i.e. Q4 = X (1-(10/11)^4)   In this case, given X was: X=9000 MT   So we have Q4 = 9,000 * (1-(10/11)^4) = 9000 * (1- 10,000/14,641) = 9,000 * (14,641-10,000)/14,641 = 9,000 * 4,641/14641 = 2852.87 rounded to 2,853 So Q4 = 2,853 MT.   Answer: 2853 MT
<result>B</result>
An iron mining company depletes 1/11 of the iron ore in a pit it mines over a year. If the company opens a new iron ore mining pit in year 1 and if the initial reserves of the pit were estimated to be 9000 MT (million tons), what is the approximate total quantity of iron ore that would have been mined from that pit by the end of year 4?