An oil company discovered an oil reserve of 140 million barrels. For time t >0,
ID: 2964737 • Letter: A
Question
An oil company discovered an oil reserve of 140 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=18 .
(a) How long does it take to exhaust the entire reserve?
time = years
(b) The oil price is a constant 50 dollars per barrel, the extraction cost per barrel is a constant 14 dollars, and the market interest rate is 8 percent per year, compounded continuously. What is the present value of the company's profit?
value = millions of dollars
Explanation / Answer
a)140=18+0.1t
t=1220 years
b)present value of profit=140*(50-14)*(1+0.08)=473.36 millions of dollars