Exercise IV: Functions of functions 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.

Exercise IV: Functions of functions 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.

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

6th Edition

ISBN:9781337111348

Author:Bruce Crauder, Benny Evans, Alan Noell

Publisher:Bruce Crauder, Benny Evans, Alan Noell

Chapter2: Graphical And Tabular Analysis

Section2.4: Solving Nonlinear Equations

Problem 27E: Water Flea F. E Smith has reported on population growth of the water flea. In one experiment, he...

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