Hi guys... can someone help me with this math question I'm trying so hard but I can't figure it out...

Question: Oil is being pumped from an oil field t years after its opening at a 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.


I am only supposed to do part c) of this question:





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?



If it helps these are the other parts:
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?
d) If the owner of the oil field decided to sell on the first day of operation, do you think the present value determined in part (c) would be a fair asking price? Explain your reasoning.


answers are:
a) P(t) = 32.5e^(0.04t) − 32.5; 4.14 billion barrels; 4.67 billion barrels
b) 12 years
c)1646.44 billion dollars
d) Answers will vary.


Thanks.

5% = 0.05

Compounded continuously means to use e^(-rt) formula to discount, where r is your interest rate (5%) and t is time.

So the equation is:

112 int 1.3 e^(0.04t) e^(-0.05t) dt , where t=0...12

0...12, because the question asks for the present value of the income stream over the period of operation of the field, which is 12 years (this is from part b).

http://www.wolframalpha.com/input/?i...t+t%3D0.. .12

The question would be more straight forwards if it said, "where T is the time found in part (b)".

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