Question

An oil well in Texas, USA produces 426 barrels in its first day of production. Its production decreases by 0.1% each day. If there are 42 gallons in one barrel of oil, and how many gallons this well will produce before it runs dry

Answer 1

The number of gallons this well will produce before it runs out is 1.789 x 10⁷ gallons.

The given parameters;

• number of barrels produced in the first day, a = 426 barrels

• decrease percent in production, = 0.1%

• 42 gallons = 1 barrel

The number of gallons this well will produce before it runs out is calculated from sum of sequence.

• the rate of the this production, r = 100% - 0.1% = 99.9% = 0.999

The sum of barrels produced is calculated as;

$s_n = \frac{a}{1-r} = \frac{426}{1-0.999} = 426,000 \ barrels$

The equivalent of this barrels in gallons is calculated as;

$= 426,000 \ barrels\ \times \frac{42 \ gallons}{barrel} \\\\= 1.789 \times 10^{7} \ gallons$

Thus, the number of gallons this well will produce before it runs out is 1.789 x 10⁷ gallons.

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