An oil company discovered an oil reserve of 100 million barrels. For time , in years, the company's extraction plan is a linear declining function of time as follows:

where is the rate of extraction of oil in millions of barrels per year at time and and .
(a) How long does it take to exhaust the entire reserve?
time = years

(b) The oil price is a constant 40 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?

Question

An oil company discovered an oil reserve of 100 million barrels. For time , in years, the company's extraction plan is a linear declining function of time as follows:

where   is the rate of extraction of oil in millions of barrels per year at time   and   and  .
(a) How long does it take to exhaust the entire reserve? 
time =  years

(b) The oil price is a constant 40 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?