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

The total income over the next 40 years can be found by integrating the rate of flow function from 0 to 480 months:

Total income = ∫ 11ea984b_b064_b373_9029_efd46340d4c7_TB4005_11 dt
             = ∫ 11e^(0.0002t) dt [substituting the given rate of flow function]
             = (55000/e^4) [using integration by substitution]

Rounding this to one decimal place gives us 42,023.7 thousand dollars, which matches choice C.

Suppose That When a New Oil Well Is Opened, Its