View image and solve question 2. ### Appliance Value Depreciation**Function Description:**If an appliance is used for a total of $ N $ hours, its value $ V $ (in hundreds of dollars) is determined by the function:\[V(N) = \left( \frac{2N + 820}{N + 2} \right)^{2/3}\]Additionally, the total number of hours $ N $ that the appliance has been used is based on the number of years $ t $ it has been in operation, following:\[ N(t) = 120t - 16t^{3/2} \]**Problems to Solve:**1. **Initial Value:** - Determine the initial value of the appliance. Provide an approximation with two significant digits.2. **Usage After 1000 Hours:** - Calculate how many years it takes to accumulate 1000 hours of use. Despite using a calculator, ensure the number is exact. - Find the value of the appliance after 1000 hours and approximate it to two significant digits.3. **Derivative $ V'(N) $:** - Express $ V'(N) $ in terms of $ N $ only and simplify as much as possible.4. **Derivative $ N'(t) $:** - Express $ N'(t) $ in terms of $ t $.5. **Rate of Change:** - Determine the instantaneous rate of change of the value function $ V $ in terms of $ t $ and $ N(t) $.6. **Value Rate at 9 Years:** - Find the rate at which the appliance value changes after 9 years. Approximate the result with two significant digits and interpret the outcome.

And Nt=120t-160t32 Where, t is the number of years it has been in operations.

If an appliance is used for a total of N hours, then its value V (in hundreds of dollars) is given by the function 2N + 820\ 2/3 V(N) = (N+2 Furthermore, suppose that the total number of hours N that the appliance has been used is based on the number of years t it has been in operation, in such a way that N(t) = 120t – 16t3/2. 1. What is the initial value of the appliance? Give an approximation with two signifi- cant digits. 2. We stop using the appliance after a total of 1000 hours. How many years does this correspond to? You can use a calculator to find this, but give the exact number. What is the value of the appliance at this point? Give an approximation with two significant digits.

If an appliance is used for a total of N hours, then its value V (in hundreds of dollars) is given by the function 2N + 820\ 2/3 V(N) = (N+2 Furthermore, suppose that the total number of hours N that the appliance has been used is based on the number of years t it has been in operation, in such a way that N(t) = 120t – 16t3/2. 1. What is the initial value of the appliance? Give an approximation with two signifi- cant digits. 2. We stop using the appliance after a total of 1000 hours. How many years does this correspond to? You can use a calculator to find this, but give the exact number. What is the value of the appliance at this point? Give an approximation with two significant digits.

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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Question

View image and solve question 2.

### Appliance Value Depreciation

**Function Description:**

If an appliance is used for a total of $ N $ hours, its value $ V $ (in hundreds of dollars) is determined by the function:

\[
V(N) = \left( \frac{2N + 820}{N + 2} \right)^{2/3}
\]

Additionally, the total number of hours $ N $ that the appliance has been used is based on the number of years $ t $ it has been in operation, following:

\[
N(t) = 120t - 16t^{3/2}
\]

**Problems to Solve:**

1. **Initial Value:**
- Determine the initial value of the appliance. Provide an approximation with two significant digits.

2. **Usage After 1000 Hours:**
- Calculate how many years it takes to accumulate 1000 hours of use. Despite using a calculator, ensure the number is exact.
- Find the value of the appliance after 1000 hours and approximate it to two significant digits.

3. **Derivative $ V'(N) $:**
- Express $ V'(N) $ in terms of $ N $ only and simplify as much as possible.

4. **Derivative $ N'(t) $:**
- Express $ N'(t) $ in terms of $ t $.

5. **Rate of Change:**
- Determine the instantaneous rate of change of the value function $ V $ in terms of $ t $ and $ N(t) $.

6. **Value Rate at 9 Years:**
- Find the rate at which the appliance value changes after 9 years. Approximate the result with two significant digits and interpret the outcome.

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