An oil company discovered an oil reserve of 100 million barrels. For time t > 0, in years, the companys 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 = 0.1 and a = 10. (a) How long does it take to exhaust the entire reserve? (b) The oil price is a constant $20 per barrel, the extraction cost per barrel is a constant $10, and the market interest rate is 10% per year, compounded continuously. What is the present value of the companys profit?

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