Problema Solution
An oil well currently produces 5 million gallons of oil per year, but the well is drying up and each year it will produce 60% of what it did the year before. How much oil can be produced from the well before it is completely dry?
Answer provided by our tutors
we take this as a geometric series with initial value 5 million, and we want the final value to be equal to 0
let 'y' represent the number of years the well has produced... the year in which the well runs dry can not really be calculated by losing 60% per year means there is "always something left (40% of whatever was there before, to be exact)"
so we decide that the well is effectively dry when it produces less than 1 barrel of oil per year, therefore we solve for 2.e-7
2.e-7 = 5 * (0.6)^(y-1)
we find that after 34 years, the well will produce less than 1 barrel of oil per year