A gold mine has 5% depletion rate. i.e. after each year of mining, the miners extract 5/100 of the mine's ore. If the current quantity of the gold reserves of the mine is currently estimated at 2 tons, how much gold would the miners be able extract over the next 4 years?	Choices:
A) 0.400 tons B) 0.200 tons C) 0.175 tons D) 0.160 tons E) 0.185 tons
X is the quantity of gold reserves of the mine   After a year of mining the quantity of gold left would be X1=X-5/100X i.e. X1=95/100X   Same thing for X2, X3, X4, respectively representing the quantity of gold left after 2, 3, 4 years of mining.   So we have:   X1=95/100 X   X2=95/100 X1   X3=95/100 X2   X4=95/100 X3   By multiplying both ends of the equations we get:   X1*X2*X3*X4 = (95/100)^4 X*X1*X2*X3   Simplification leaves us with:   X4 = (95/100)^4 X   X4 is the quantity of gold left after four years of mining. So the cumulative quantity of gold (Q4) which has been extracted after 4 years is: Q4= X-X4=X-(95/100)^4X i.e. Q4 = X (1-(95/100)^4)   In this case, given X was: X=2 tons   So Q4 = 2 * (1-(95/100)^4) = 2 * (1-81450625/10^8) =2 * 18549375/10^8 = 0.1854 tons round to Q4=0.185 ton   Answer 0.185 tons.
<result>E</result>
A gold mine has 5% depletion rate. i.e. after each year of mining, the miners extract 5/100 of the mine's ore. If the current quantity of the gold reserves of the mine is currently estimated at 2 tons, how much gold would the miners be able extract over the next 4 years?