Calculus: Graphical, Numerical, Algebraic

3rd Edition

ISBN: 9780133688399

Author: Finney, Ross L.

Publisher: Pearson/Prentice Hall

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Question

Chapter 3.3, Problem 52E

To determine

To find: The current instantaneous rate of change in each number’ share of the pavilion rental fee.

Expert Solution & Answer

Answer to Problem 52E

The share of each of the member decreases to −$0.20 .

Explanation of Solution

Given Data:

The number of members 65 members and the pavilion rents for $250.

The pavilion cost is increasing at the rate of $10 per year.

The blue boar membership increase at the rate of 6 members per year.

Calculation:

Consider the function for the number of members years from now is m(x) .

Consider the function for the number pavilion cost x years from now.

From the given equation.

m(0)=65c(0)=$250m′(0)=6c′(0)=$10

Consider the rate of change of each number is,

d(cm)dx=m(0)d(c(0))dx−c(0)d(m(0))dx(m(0))2=m(0)c′(0)−c(0)m′(0)(m(0))2

Then,

m(0)c′(0)−c(0)m′(0)(m(0))2=65(10)−250(6)(65)2=−$0.20

The share of each of the member decreases to −$0.20 .

Chapter 3.3, Problem 51E

Chapter 3.3, Problem 53E

Chapter 3 Solutions

Calculus: Graphical, Numerical, Algebraic

Ch. 3.1 - Prob. 1QR Ch. 3.1 - Prob. 2QR Ch. 3.1 - Prob. 3QR Ch. 3.1 - Prob. 4QR Ch. 3.1 - Prob. 5QR Ch. 3.1 - Prob. 6QR Ch. 3.1 - Prob. 7QR Ch. 3.1 - Prob. 8QR Ch. 3.1 - Prob. 9QR Ch. 3.1 - Prob. 10QR

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