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?
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Check your signs - the formula should have Q(t) decreasing with time, not increasing. You should have:
If you set t to infinity you get:
Set to determine the minimum value of k in terms of and that satisfies the condition.
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