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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