1. Velocity/Net-Change type word problem

Here is the problem (51):

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?

2. 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.