An oil company discovered an oil reserve of 100 million barrels.?

Question

For time t > 0, in years, the company’s extraction plan is a linear declining function of time as follows:
,
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) If it takes 10.6 years to exhaust the reserve and 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?

Answer 1

The function q(a,b,t) for the extraction plan has disappeared from your question, so nobody can answer it for you.

Answer 2

The answer is drill in Alaska

Answer 3

Sign it over to me, here's my bank data...