# math

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The amounts of oil pumped from an oil well in each of the years 2001 to 2004 formed a geometric progression with common ratio 0.9. The amount pumped in 2001 was 100000 barrels.

Calculate in which year the amount pumped will fall below 5000.

The amounts of oil pumped from an oil well in each of the years 2001 to 2004 formed a geometric progression with common ratio 0.9. The amount pumped in 2001 was 100000 barrels.

Calculate in which year the amount pumped will fall below 5000

The last term of a geometric series is given by L = ar^(n-1)where a = the first term, r = the common ration and n = the number of terms.

Here, 5000 = 100,000(.9)^(n-1)

.05 = =.9^(n-1)

log(.05) = =log(.9)(n-1)

-.13010299 = -.04575 (n-1)

28.433 = (n-1) making n = 29.433

Therefore, less than 5000 barrels will be pumped in the year 2031 (2001 + 30)

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