Question: An oil company discovered an oil reserve of 100 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 = 0.1 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 company's profit?