Question: The revenue produced by a new oil well is $1 million per year initially (t = 0), which is expected to rise uniformly to $5 million per year after 10 years. If we measure time in years and let f (t) denote the revenue (in millions of dollars) per unit of time at time t, it follows that f (t) = 1+0.4t. If F (t) denotes the total revenue that accumulates over the time interval [0, t], then F (t) = f (t).
(a) Calculate the total revenue earned during the 10 year period (i.e. F (10)).
(b) Find the present value of the revenue stream over the time interval [0, 10], if we assume continuously compounded interest at the rate r = 0.05 per year.