An oil company discovered an oil reserve of 130 million barrels. For time t>0, i

Question

An oil company discovered an oil reserve of 130 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=0.15 and a=14

(a) How long does it take to exhaust the entire reserve?

(b) The oil price is a constant 50 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

q(t)= a-bt integrate 0 to t q(t)=130 14t-0.2t^2=130 t=11 years or 59 years b.) profit= 50-10=40$ A= 40(1.1)^t

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