an oil company discovered an oil reserve of 170 million barrels. for time t>0, i

Question

an oil company discovered an oil reserve of 170 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-bt, where q(t) is the rate of extraction of oil in millions of barrels per year at time t and b= .2 and a= 10. how long does it take to exhaust the entire reserve?The oil price is a constant 45 dollars per barrel, the extraction cost per barrel is a constant 10 dollars, and the market interest rate is 10 percent per year, compounded continuously. What is the present value of the company's profit?

Explanation / Answer

Integrate the problem on both sides. dQ/dt=a-bt. After integration on both sides, Q(t)=at-bt^2/2+170. Now, to exhaust entire vessel, Q(t)=0. Solve the quadratic equation and you will get the answer. answer=114.8 years.

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