Is it possible to Clarify the following Bartleby Expert Answer, with any Signs (/, *, +,-) and/or Positions (^, XY, Xy) that may be helpful? Thank you! (Original Question is also provided). Original Question: 2. A small oil company considers the continuous pumping of oil from a well as a continuous income stream, f(t) = 600e-02: in thousands of dollars per year. (a) (10) Find an estimate of the total income from this well over the next 10 years.
Is it possible to Clarify the following Bartleby Expert Answer, with any Signs (/, *, +,-) and/or Positions (^, XY, Xy) that may be helpful? Thank you! (Original Question is also provided). Original Question: 2. A small oil company considers the continuous pumping of oil from a well as a continuous income stream, f(t) = 600e-02: in thousands of dollars per year. (a) (10) Find an estimate of the total income from this well over the next 10 years.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
![**Step 2**
(a) Given that the income is \( f(t) = 600e^{-0.2t} \) in thousand dollars per year.
The total income over the next 10 years is given by the integral over 0 to 10 of \( f \).
Then,
\[
\text{Total income} = \int_0^{10} f(t) \, dt = \int_0^{10} 600e^{-0.2t} \, dt = 600e^{-0.2t} \Big|_0^{10} = 600 \cdot (-0.2) \cdot \left(0.2 \cdot 10 \right) - 0.2 \cdot 0 = -3000e^{-2} - 1 = 3000(1 - e^{-2}) = 2593.99
\]
Hence, the total income from the well over the next 10 years will be **2593.99 thousand dollars**.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6274a625-9a74-4008-b392-f1961eea52c4%2F95faaafa-a4c5-4930-ac34-139d6c598d25%2Fbv25bu_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Step 2**
(a) Given that the income is \( f(t) = 600e^{-0.2t} \) in thousand dollars per year.
The total income over the next 10 years is given by the integral over 0 to 10 of \( f \).
Then,
\[
\text{Total income} = \int_0^{10} f(t) \, dt = \int_0^{10} 600e^{-0.2t} \, dt = 600e^{-0.2t} \Big|_0^{10} = 600 \cdot (-0.2) \cdot \left(0.2 \cdot 10 \right) - 0.2 \cdot 0 = -3000e^{-2} - 1 = 3000(1 - e^{-2}) = 2593.99
\]
Hence, the total income from the well over the next 10 years will be **2593.99 thousand dollars**.
![**New Question:**
Is it possible to clarify the following Bartleby Expert Answer, with any **Signs** (/, *, +, −) and/or **Positions** (^, Xⁿ, Xᵧ) that may be helpful? Thank you! (Original Question is also provided).
**Original Question:**
2. A small oil company considers the continuous pumping of oil from a well as a continuous income stream,
\[ f(t) = 600e^{-0.2t} \]
in thousands of dollars per year.
(a) (10) Find an estimate of the total income from this well over the next 10 years.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6274a625-9a74-4008-b392-f1961eea52c4%2F95faaafa-a4c5-4930-ac34-139d6c598d25%2F3yrdbch_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**New Question:**
Is it possible to clarify the following Bartleby Expert Answer, with any **Signs** (/, *, +, −) and/or **Positions** (^, Xⁿ, Xᵧ) that may be helpful? Thank you! (Original Question is also provided).
**Original Question:**
2. A small oil company considers the continuous pumping of oil from a well as a continuous income stream,
\[ f(t) = 600e^{-0.2t} \]
in thousands of dollars per year.
(a) (10) Find an estimate of the total income from this well over the next 10 years.
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