make sure you do it in a white paper. do not type it **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.

Given: A company bought a machine for $475000. It depreciates at a rate of 30% per year. To find…

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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make sure you do it in a white paper. do not type it

**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.

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