Question

Crude oil is leaking from a tank at the rate of 10% of the tank volume every 3 hrs. If the tanker originally contained 500,000 gallons of oil, how many gallons of oil remain in the tank after 4 hrs? Round to the nearest gallon.

Answer 1

434,470 gallons

Explanation:

The exponential equation for the volume v remaining after t hours can be written as ...

v(t) = (initial amount)×(decay factor)^(t/(decay time))

v(t) = 500,000×(1 -10%)^(t/3)

Then after 4 hours, the remaining volume is ...

v(4) = 500,000×(0.90^(4/3)) ≈ 434,470 . . . . gallons

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Comment on the form of the equation

The decay factor is related to the decay rate by ...

decay factor = 1 - (decay rate)

and the decay time is the time applicable to that decay rate. Here, the rate is 10% every 3 hours, so the decay time is 3 hours for a decay rate of 10%.