SOLUTION: A fuel reservoir tank can hold 1200 liters of fuel at full capacity. Due to a breach, a small leak has been reported in the reservoir tank. Site engineers have recorded the rate o

Algebra ->  Test -> SOLUTION: A fuel reservoir tank can hold 1200 liters of fuel at full capacity. Due to a breach, a small leak has been reported in the reservoir tank. Site engineers have recorded the rate o      Log On


   

Question 1161018: A fuel reservoir tank can hold 1200 liters of fuel at full capacity. Due to a breach, a small leak has been
reported in the reservoir tank. Site engineers have recorded the rate of leakage as f(t) =
6e
−0.1t
liters per minute. During the breach, fuel’s level transmitter was broken, and it is estimated
that repair team will require one and half hour to repair the reservoir. You have been tasked to
calculate the amount of fuel left in the reservoir by the time repair work is completed. Show all steps.
Answer by ikleyn(52852) About Me  (Show Source):
You can put this solution on YOUR website!
.

The volume of the leakage is the integral of the function  6e%5E%28-0.1t%29 over the time from t= 0 to t= 90 minutes.


This integral is equal to  %28-6%2F0.1%29%2A%28e%5E%28-9%29-1%29 = 60%2A%281-e%5E%28-9%29%29 = 60%2A%281-2.71828%5E%28-9%29%29 = 60*(1-0.000123) = 60 liters

    (with the accuracy absolutely enough for any engineering purposes).



By knowing the leakage volume, you calculate the amount of fuel left in the reservoir as the difference

    1200 liters - 60 liters = 1140 liters.    ANSWER



Notice that starting leakage rate was  6 liters per minute.


At the time t= 90 minutes, the leakage rate is  6e%5E%28-9%29 = 6%2A2.71828%5E%28-9%29 = 0.00074 liters per minute.


So, the change of the leakage rate during 90 minutes is very significant.