An oil company discovered an oil reserve of 120 million barrels. For time $t > 0$, in years, the company's extraction plan is a linear declining function of time as follows: $$q (t) = a - b t,$$ where $q(t)$ is the rate of extraction of oil in millions of barrels per year at time $t$ and $b = 0.15$ and $a = 12$ .

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

(b) The oil price is a constant 45 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?

value = millions of dollars