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Problem 81 Hard Difficulty

An oil storage tank ruptures at time $ t = 0 $ and oil leaks from the tank at a rate of $ r(t) = 100e^{-0.01t} $ liters per minute. How much oil leaks out during the first hour?

Answer

4512 liters

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Video Transcript

have a question ah in this it is given that the oil is tourist tank ruptures at equal to zero. That is People to zero. It starts leaking an oil leak from the tank at a rate of so rate of oil leaking is equal to 100 Areas to the Power -0.01 T Letters. But a minute. So how much I like it. This is the rate of our licking. So let us write it as D. V. By DT. That is volume because volumizing leaders. So that is this is the rate of decreasing, decreasing of volume for tv by DT equal to it is given it like this but Dave ability should be negative as it is leaking so volume will be decreasing. So we should write D by D. T. Equal to minus 100 areas of the power -0.01. The so D. B will be equal to minus and did areas to the power minus 0.0 and T. D. T. Now we have to integrate to get all the values. So integrating that went equal to zero Like it had just started. So it should be zero Went equal to first hour, that is 16 minutes. This is the which means volume will be called to minus hinted From limited 0 to 60. Areas of the Power -0.01 T. Mhm. So this is mine is ended. Here is the power -0.01. T divide by minus 0.01 from limit 0 to 60. This will be minus and minus will become place hunted by 0.01. and areas to the power -0.01 T from 0 to 60. Okay, This will become 10,000. And let us start plugging in the limits -0.01 into 60- It is to the power -0.01 in 20. Okay, so 10,000 and it is the power it would become it is really power uh -0.6 you have to use and collected. It is the power the he used to be published minus blind stick and minus one -15 into 1000 king. Yeah. Okay let's do it again. It is the bottom line is sick and then it is to the farmers minus but I'm sick minus one into and tell him this is 4000 500 11 point aided with negative side later 10 shoulder. This much volume is lost or leaked during the first star approximately it is 4511 point 88 liters. Thank you