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 a 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?
A profit function and present and future values of an income stream are investigated. The solution is detailed and well presented.