Suppose that when a new oil well is opened, its production is viewed as a continuous income stream with monthly rate of flow where t is time in months and f is in thousands of dollars per month. Find the total income over the next 40 years (480 months). Round your answer to one decimal place.
A) 41,776.7 thousand dollars
B) 99,623.7 thousand dollars
C) 42,023.7 thousand dollars
D) 61,203.7 thousand dollars
E) 118,823.7 thousand dollars

Question

Suppose that when a new oil well is opened, its production is viewed as a continuous income stream with monthly rate of flow  where t is time in months and f is in thousands of dollars per month. Find the total income over the next 40 years (480 months). Round your answer to one decimal place. ​
A) 41,776.7 thousand dollars 
B) 99,623.7 thousand dollars 
C) 42,023.7 thousand dollars 
D) 61,203.7 thousand dollars 
E) 118,823.7 thousand dollars

Quizplus · Accepted Answer

To find the total income over the next 40 years, we need to integrate the given rate of flow function from 0 to 480 months:

∫(0 to 480) 11ea984b_b142_904e_9029_ebce3ed5f988_TB4005_11 dt

= 11ea984b_b142_904e_9029_ebce3ed5f988_TB4005_11 ∫(0 to 480) e^(0.0002t) dt (using the fact that e^ln(x) = x)

= 11ea984b_b142_904e_9029_ebce3ed5f988_TB4005_11 [5000(e^0.0002t)](0 to 480)

= 11ea984b_b142_904e_9029_ebce3ed5f988_TB4005_11 (5000)(e^0.096) - 5000

≈ 42,023.7 thousand dollars (rounded to one decimal place)

Therefore, the best choice is C.

Suppose That When a New Oil Well Is Opened, Its