document.write( "Question 1161018: A fuel reservoir tank can hold 1200 liters of fuel at full capacity. Due to a breach, a small leak has been
\n" ); document.write( "reported in the reservoir tank. Site engineers have recorded the rate of leakage as f(t) =
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\n" ); document.write( "−0.1t
\n" ); document.write( "liters per minute. During the breach, fuel’s level transmitter was broken, and it is estimated
\n" ); document.write( "that repair team will require one and half hour to repair the reservoir. You have been tasked to
\n" ); document.write( "calculate the amount of fuel left in the reservoir by the time repair work is completed. Show all steps. \n" ); document.write( "

Algebra.Com's Answer #784448 by ikleyn(52858) $\"\"$ $\"About$

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document.write( "The volume of the leakage is the integral of the function   over the time from t= 0 to t= 90 minutes.\r\n" );
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document.write( "This integral is equal to   =  =  = 60*(1-0.000123) = 60 liters\r\n" );
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document.write( "    (with the accuracy absolutely enough for any engineering purposes).\r\n" );
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document.write( "By knowing the leakage volume, you calculate the amount of fuel left in the reservoir as the difference\r\n" );
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document.write( "    1200 liters - 60 liters = 1140 liters.    ANSWER\r\n" );
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document.write( "Notice that starting leakage rate was  6 liters per minute.\r\n" );
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document.write( "At the time t= 90 minutes, the leakage rate is   =  = 0.00074 liters per minute.\r\n" );
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document.write( "So, the change of the leakage rate during 90 minutes is very significant.\r\n" );
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