A company buys a machine for $475,000 that depreciates at a rate of 30% per year. Find a formula for the value of the machine after n years. V(n) = 475000(0.7)" What is its value after 7 years? (Round your answer to two decimal places.) $ X
A company buys a machine for $475,000 that depreciates at a rate of 30% per year. Find a formula for the value of the machine after n years. V(n) = 475000(0.7)" What is its value after 7 years? (Round your answer to two decimal places.) $ X
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![**Depreciation of a Machine: Calculating Future Value**
A company buys a machine for **$475,000** that depreciates at a rate of **30%** per year. To determine the value of the machine after \( n \) years, use the formula:
\[ V(n) = 475000 \times (0.7)^n \]
**Formula Explanation:**
- **\( 475000 \)**: Initial purchase price of the machine.
- **\( 0.7 \)**: Represents the remaining value after 30% depreciation (i.e., 100% - 30% = 70%, or 0.7 in decimal form).
- **\( n \)**: Number of years the machine has depreciated.
**Question:** What is its value after **7 years**? (Round your answer to two decimal places.)
- **Answer Box:** Incorrect notation indicating the answer needs to be calculated and entered.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F07f64844-f44f-4fd0-96ac-4d29f63737de%2F5970210d-25ac-4bfe-8b98-786c2dd1cfa3%2Ft5id6yr_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Depreciation of a Machine: Calculating Future Value**
A company buys a machine for **$475,000** that depreciates at a rate of **30%** per year. To determine the value of the machine after \( n \) years, use the formula:
\[ V(n) = 475000 \times (0.7)^n \]
**Formula Explanation:**
- **\( 475000 \)**: Initial purchase price of the machine.
- **\( 0.7 \)**: Represents the remaining value after 30% depreciation (i.e., 100% - 30% = 70%, or 0.7 in decimal form).
- **\( n \)**: Number of years the machine has depreciated.
**Question:** What is its value after **7 years**? (Round your answer to two decimal places.)
- **Answer Box:** Incorrect notation indicating the answer needs to be calculated and entered.
![**Problem Statement:**
Find the sum of the convergent series. (Round your answer to four decimal places.)
\[
\sum_{n=1}^{\infty} (\sin(1))^n
\]
**Instructions:**
To solve this problem, you need to evaluate the infinite geometric series where the common ratio \( r = \sin(1) \).
**Concepts:**
- **Convergent Series:** A series that approaches a finite limit as the number of terms goes to infinity.
- **Geometric Series Sum Formula:** For a geometric series \(\sum_{n=0}^{\infty} ar^n\) with \(|r| < 1\), the sum is given by:
\[
S = \frac{a}{1-r}
\]
where \( a \) is the first term of the series and \( r \) is the common ratio.
**Application:**
In this example, set \( a = \sin(1) \) and \( r = \sin(1) \). Calculate the sum using the formula for the geometric series sum, rounding the final answer to four decimal places.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F07f64844-f44f-4fd0-96ac-4d29f63737de%2F5970210d-25ac-4bfe-8b98-786c2dd1cfa3%2Fyzxjzrl_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Find the sum of the convergent series. (Round your answer to four decimal places.)
\[
\sum_{n=1}^{\infty} (\sin(1))^n
\]
**Instructions:**
To solve this problem, you need to evaluate the infinite geometric series where the common ratio \( r = \sin(1) \).
**Concepts:**
- **Convergent Series:** A series that approaches a finite limit as the number of terms goes to infinity.
- **Geometric Series Sum Formula:** For a geometric series \(\sum_{n=0}^{\infty} ar^n\) with \(|r| < 1\), the sum is given by:
\[
S = \frac{a}{1-r}
\]
where \( a \) is the first term of the series and \( r \) is the common ratio.
**Application:**
In this example, set \( a = \sin(1) \) and \( r = \sin(1) \). Calculate the sum using the formula for the geometric series sum, rounding the final answer to four decimal places.
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