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 rate of flow function from 0 to 480 (in months), and multiply the result by 1000.

∫(11e^(-0.05t))dt from 0 to 480 ≈ 42,023.7

Multiplying by 1000 gives us the answer in thousands of dollars:

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