A small oil company considers the continuous pumping of oil from a well as a continuous income stream, f(t)=600e- e-0.2t in thousands of dollars per year. Suppose that the oil company is planning to sell the well. The company establish its selling price using the present value' of this well over the next 10 years. b. If the income can be invested at 10% compounded continuously, what is the estimated selling price of this well?
A small oil company considers the continuous pumping of oil from a well as a continuous income stream, f(t)=600e- e-0.2t in thousands of dollars per year. Suppose that the oil company is planning to sell the well. The company establish its selling price using the present value' of this well over the next 10 years. b. If the income can be invested at 10% compounded continuously, what is the estimated selling price of this well?
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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![Certainly! The text from the image is as follows:
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**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.
Suppose that the oil company is planning to sell the well. The company establishes its selling price using the 'present value' of this well over the next 10 years.
**b.** If the income can be invested at 10% compounded continuously, what is the estimated selling price of this well?
---
**Explanation:**
The equation \( f(t) = 600e^{-0.2t} \) represents the continuous income stream from pumping oil, measured in thousands of dollars per year. Here, \( t \) is time in years, and the function models the income as it decreases exponentially over time.
The problem involves calculating the present value of the income stream over a 10-year period if the income were invested at a continuous compound interest rate of 10%. This requires integrating the income function over the 10-year period and applying the formula for present value with continuous compounding.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6274a625-9a74-4008-b392-f1961eea52c4%2F64d3d491-c8d2-4b84-8c64-beb8b0f26f1b%2Fepnmih6_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Certainly! The text from the image is as follows:
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**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.
Suppose that the oil company is planning to sell the well. The company establishes its selling price using the 'present value' of this well over the next 10 years.
**b.** If the income can be invested at 10% compounded continuously, what is the estimated selling price of this well?
---
**Explanation:**
The equation \( f(t) = 600e^{-0.2t} \) represents the continuous income stream from pumping oil, measured in thousands of dollars per year. Here, \( t \) is time in years, and the function models the income as it decreases exponentially over time.
The problem involves calculating the present value of the income stream over a 10-year period if the income were invested at a continuous compound interest rate of 10%. This requires integrating the income function over the 10-year period and applying the formula for present value with continuous compounding.
![**Preceding Question:**
A small oil company considers the continuous pumping of oil from a well as a continuous income stream, given by the function:
\[ f(t) = 600e^{-0.2t} \]
where \( f(t) \) is the income in thousands of dollars per year.
**(a)** Find an estimate of the total income from this well over the next 10 years.
**Expert Solution**
**Step 2**
To find the estimated total income over the next 10 years, we calculate:
\[
f(10) = 600 \times e^{-0.2 \times 10}
\]
\[
= 600 \times e^{-2}
\]
\[
= 600 \times \frac{1}{e^2}
\]
\[
= \frac{600}{(2.7183)^2}
\]
\[
\approx 81.2000
\]
So, the total income over the next 10 years is \(\boxed{81.20}\) thousand dollars.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6274a625-9a74-4008-b392-f1961eea52c4%2F64d3d491-c8d2-4b84-8c64-beb8b0f26f1b%2Ft7fd6fa_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Preceding Question:**
A small oil company considers the continuous pumping of oil from a well as a continuous income stream, given by the function:
\[ f(t) = 600e^{-0.2t} \]
where \( f(t) \) is the income in thousands of dollars per year.
**(a)** Find an estimate of the total income from this well over the next 10 years.
**Expert Solution**
**Step 2**
To find the estimated total income over the next 10 years, we calculate:
\[
f(10) = 600 \times e^{-0.2 \times 10}
\]
\[
= 600 \times e^{-2}
\]
\[
= 600 \times \frac{1}{e^2}
\]
\[
= \frac{600}{(2.7183)^2}
\]
\[
\approx 81.2000
\]
So, the total income over the next 10 years is \(\boxed{81.20}\) thousand dollars.
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