Chapter 2.7, Problem 48E

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8th Edition

James Stewart

ISBN: 9781305270343

Textbook Problem

The number *N* of locations of a popular coffeehouse chain is given in the table. (The numbers; of locations as of October 1 are given.)

Year | 2004 | 2006 | 2008 | 2010 | 2012 |

N |
8569 | 12,440 | 16,680 | 16,858 | 18,066 |

(a) Find the average rate of growth

(i) from 2006 to 2008

(ii) from 2008 to 2010

In each case, include the units. What can you conclude?

(b) Estimate the instantaneous rate of growth in 2010 by taking the average of two average rates of change. What are *its* units?

(c) Estimate the instantaneous rate of growth in 20!0 by measuring the slope of a tangent.

(a)

To determine

**To find:** The average rate of growth

Explanation

**Given:**

Let *t*, where *t* is in years.

**Formula used:**

The average rate of growth *N* with respect to *t* on the interval

**Calculation:**

**Section (i)**

Obtain the average rate of growth

Substitute 2006 for

Consider the given table, the values of

Thus, the average rate of growth

(b)

To determine

**To estimate:** The instantaneous rate of growth of

(c)

To determine

**To estimate:** The instantaneous rate of growth in 2010 by measuring the slope of the tangent.

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