# (The numbers of locations as of October 1 are given.)

**Question description**

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 | 2005 | 2006 | 2007 | 2008 |
---|---|---|---|---|---|

N | 8575 | 10,244 | 12,443 | 15,007 | 16,678 |

(a) Find the average rate of growth between each pair of years.

2004 to 2006 | locations/year |

2006 to 2007 | locations/year |

2005 to 2006 | locations/year |

(b) Estimate the instantaneous rate of growth in 2006 by taking the average of the last two rates of change in part (a).

locations/year

(c) Estimate the instantaneous rate of growth in 2006 by measuring the slope of the tangent line through

locations/year

(d) Estimate the instantaneous rate of growth in 2007 by measuring the slope of the tangent line through

(2006, 12443) and (2008, 16678). location/year

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