BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805
BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

Solutions

Chapter 2, Problem 41RE
To determine

To find:The value of C'(1990) .

Expert Solution

Answer to Problem 41RE

The value of C'(1990) is estimated as total value of the currency was increasing at a rate of approximately $22.2 billion dollars per year.

Explanation of Solution

Given information:

The given table is.

  Single Variable Calculus: Concepts and Contexts, Enhanced Edition, Chapter 2, Problem 41RE

Calculation:

First row of the table shown below is time, in years, and the second row is the total value of currency, in billions of dollars.

The value of C'(1990) is by the definition,

  C'(1990)=limt1990C(t)C(1990)t1990

Using the value of t given in table which are closet to 1990 ,

  C'(1990)=C(1985)C(1990)19851990=187.3271.95=16.92

Calculate another estimate.

  C'(1990)=C(1995)C(1990)19951990=409.3271.95=27.48

This is reasonable to assume that the average of these two numbers is a good estimate.

  C'(1990)=16.92+27.482=22.2billiondollars/yr

This derivative measures the rate of change of C , so in 1990 the total value of the currency was increasing at a rate of approximately $22.2 billion dollars per year.

Therefore, the value of C'(1990) is estimated as total value of the currency was increasing at a rate of approximately $22.2 billion dollars per year.

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