Oil is being pumped from an oil field t years after its opening at the rate of P'(t) = 1.3e^0.04t billion barrels per year. The field has a reserve of 20 billion barrels, and the price of oil holds steady at $112 per barrel.

a. Find P(t), the amount of oil pumped from the field at time t. How much oil is pumped from the field during the first 3 years of operation? The next 3 years?

b. For how many years T does the field operate before it runs dry?

c. If the prevailing annual interest rate stays fixed at 5% compounded continuously, what is the present value of the continuous income stream V = 112P(t) over the period of operation of the field 0 ≤ t ≤ T?