Question: Let P be the total petroleum reservoir on Earth in the year t. (In other words, P represents the total quantity of petroleum, including what's not yet discovered, on Earth at time t.) Assume that no new petroleum is being made and that P is measured in barrels. What are the units of dP/dt? What is the meaning of dP/dt? What is its sign? How would you set about estimating this derivative in practice? What would you need to know to make such an estimate?