Final answer:
The question is regarding the mathematical model for the depletion of an oil reserve using a linear declining function over time, situated within the broader context of historical oil consumption and discovery rates.
Step-by-step explanation:
The question pertains to the mathematical modeling of the extraction of an oil reserve, specifically by using a linear declining function of time. The oil reserve has a starting quantity of 150 million barrels, and the extraction rate, a linear function q(t) = a - bt, decreases over time.
The historical context provided indicates that global oil consumption has already reached half of the conventional oil resources, with remaining reserves depleting toward an eventual scarcity. The situation of the North Sea is highlighted where oil discoveries have ceased and production is nearing an end.
Economic history is also touched upon, referencing the 1973 OPEC oil embargo and the consequent shift of the supply curve, which affected oil prices and consumption in the U.S.
The complete question is: An oil company discovered an oil reserve of 150 million barrels. For time ( t>0 in years, the company's extraction plan is a linear declining function of time as follows: [ q(t)=a-b t is: