View image and solve question 5. If an appliance is used for a total of N hours, then its value V (in hundreds of dollars) isgiven by the function2N + 820\ ²/3V(N) = N+2Furthermore, suppose that the total number of hours N that the appliance has beenused is based on the number of years t it has been in operation, in such a way thatN(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 thiscorrespond 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 twosignificant digits.3. Find V'(N) in terms of N only. Simplify as much as possible.4. Find N'(t) in terms of t.5. Find the instantaneous rate of change of the value function V in terms of t andN(t).6. At what rate is the value of the appliance changing when we have been using it for9 years? Give an approximation with two significant digits. Interpret your result.

Answered: 5. Find the instantaneous rate of…

Math

Calculus

5. Find the instantaneous rate of change of the value function V in terms of t and N(t).

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter5: Inverse, Exponential, And Logarithmic Functions

Section5.6: Exponential And Logarithmic Equations

Problem 64E

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Question

View image and solve question 5.

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.
3. Find V'(N) in terms of N only. Simplify as much as possible.
4. Find N'(t) in terms of t.
5. Find the instantaneous rate of change of the value function V in terms of t and
N(t).
6. At what rate is the value of the appliance changing when we have been using it for
9 years? Give an approximation with two significant digits. Interpret your result.

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