An oil company discovered an oil reserve of 160 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 = 0.2 and a = 14.
a. How long does it take to exhaust the entire reserve?
b. The oil price is a constant 35 dollars per barrel, the extraction cost per barrel is a constant 20 dollars, and the market interest rate is 10 percent per year, compounded continuously. What is the present value of the company's profit?