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Math Help - Velocity/Net-Change type word problem

  1. #1
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    Velocity/Net-Change type word problem

    Here is the problem (51):
    Velocity/Net-Change type word problem-2013-05-15_10-47-25_759.jpg

    I've gotten as far as finding the function that gives the future amount of oil reserves:

    Q(t)=(2*109) + 107((1 - e-kt)/k)

    I have tried working out Q(1), but solving for k is still proving difficult. Any hints?
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  2. #2
    MHF Contributor ebaines's Avatar
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    Re: Velocity/Net-Change type word problem

    Check your signs - the formula should have Q(t) decreasing with time, not increasing. You should have:

     Q(t) = Q_0 +\frac {R_0} k (e^{-kt} -1)

    If you set t to infinity you get:

     Q(\infty) = Q_0 + \frac {R_0} k (e^{-\infty} -1) = Q_0 - \frac {R_0} k

    Set  Q(\infty) = 0 to determine the minimum value of k in terms of  Q_0 and  R_0 that satisfies the condition.
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