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 600,000 gallons of oil, how many gallons of oil remain in the tank after 4 hrs? Round to the nearest gallon.

Answer 1

`\textit{Periodic/Cyclical Exponential Decay} \\\\ A=P(1 - r)^{(t)/(c)}\qquad \begin{cases} A=\textit{current amount}\\ P=\textit{initial amount}\dotfill &600000\\ r=rate\to 10\%\to (10)/(100)\dotfill &0.10\\ t=hours\dotfill &4\\ c=period\dotfill &3 \end{cases} \\\\\\ A=600000(1 - 0.10)^{(4)/(3)}\implies A=600000(0.9)^{(4)/(3)}\implies A\approx 521364`

Answer 2

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) = 600,000×(1 -10%)^(t/3)

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

v(4) = 600,000×(0.90^(4/3)) = 521364.2677 gallons