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 calculate the definite integral of the rate of flow function from 0 to 480 months.
 
∫(0 to 480) 11ea984b_b0a8_4bcc_9029_075c8e8e0cf2_TB4005_11 dt

= 11ea984b_b0a8_4bcc_9029_075c8e8e0cf2_TB4005_11 * [e^(480/1200) - e^(0/1200)]

= 11ea984b_b0a8_4bcc_9029_075c8e8e0cf2_TB4005_11 * [e^(2/5) - 1]

≈ 42023.7 thousand dollars (rounded to one decimal place)

Therefore, the best choice is C, with the total income being approximately 42,023.7 thousand dollars.

Suppose That When a New Oil Well Is Opened, Its