An oil company discovered an oil reserve of 110 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 = 0.05 and a = 10. (a) How long does it take to exhaust the entire reserve? time = years (b) The oil price is a constant 30 dollars per barrel, the extraction cost per barrel is a constant 16 dollars, and the market interest rate is 9 percent per year, compounded continuously What is the present value of the company's profit? value = millions of dollars

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