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Finding the total production of oil given a rate.

  1. Jan 29, 2012 #1
    1. The problem statement, all variables and given/known data
    Oil is flowing from a well in a continuous stream at a rate of
    f(t) =54/(t + 3)^2 barrels per month (in multiples of 100). Find
    the total oil produced by the well in its second
    three months of operation.

    2. Relevant equations



    3. The attempt at a solution
    Answer choices are 300, 250, 350, 450, 400.
    Now, I found the problem worded strangely, but here goes. f(t) is a derivative, so I took the integral of f(t) and got -54/(t+3). The question asks for how much is produced in its second three months, so I took that as 6 months total. Plug in 6 for t and get -6 barrels. But it is in multiples of 100, so 600 barrels produced in the 6 months? So if its asking for oil produced in its "second three months of operation", then in those three months it produced 300 barrels? I hate the wording of the question, and that is the only way I could interpret it and get an answer choice that was provided. Your thoughts?
     
  2. jcsd
  3. Jan 29, 2012 #2
    I take "second three months" to mean between t=4 and t=6 (where the first three are t=1 to t=3, though it's ambiguous enough that it could be between t=0 and t=2). So you evaluate the definite integral

    [tex]\int_4^6\ f(t)\ dt[/tex]
     
  4. Jan 29, 2012 #3

    Dick

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    I would integrate 5400/(t+3)^2 for t=3 to t=6. So I'd probably say 300 as well. But not quite for the reasons you give.
     
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