Question: For some constants A and B, the rate of production, R(t), of oil in a new oil well is modeled by:
R(t) = A + Be-t sin(2Πt)
Where t is the time in years, A is the equilibrium rate, and B is the "variability" coefficient.
(a) Find the total amount of oil produced in the first N years of operation. (Take N to be an integer.)
(b) Find the average amount of oil produced per year over the first N years (where N is an integer).
(c) From your answer to part (b), find the average amount of oil produced per year as N → ∞.
(d) Looking at the function R(t), explain how you might have predicted your answer to part (c) without doing any calculations.
(e) Do you think it is reasonable to expect this model to hold over a very long period? Why or why not?