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6th Edition

Stewart + 5 others

Publisher: Cengage Learning

ISBN: 9780840068071

Chapter 2.4, Problem 25E

(a)

To determine

**To find:** The average rate of change of population between 1998 and 2001.

Expert Solution

The average rate of change of water between 1998 and 2001 is 245 person/year.

**Given:**

The given table is,

Year | Population |

1997 | 624 |

1998 | 856 |

1999 | 1336 |

2000 | 1578 |

2001 | 1591 |

2002 | 1483 |

2003 | 994 |

2004 | 826 |

2005 | 801 |

2006 | 745 |

**Formula used:**

Average rate of change of function *.*

**Calculation:**

The table shows the population *P* in a small coastal community from 1997 to 2006.

From the given table the population in the year 1998 is 856 persons and the population in the year 2001 is also 1591 persons.

Substitute 856 for *a* and 2001 for *b* in equation (1),

Therefore, average rate of change of population between 1998 and 2001 is 245 person/year.

(b)

To determine

**To find:** The average rate of change of population between 2002 and 2004.

Expert Solution

The average rate of change of Population between 2002 and 2004 is

**Given:**

The given table is,

Year | Population |

1997 | 624 |

1998 | 856 |

1999 | 1336 |

2000 | 1578 |

2001 | 1591 |

2002 | 1483 |

2003 | 994 |

2004 | 826 |

2005 | 801 |

2006 | 745 |

**Calculation:**

The table shows the population *P* in a small coastal community from 2002 to 2004.

From the given table the population in the year 1998 is 856 persons and the population in the year 2001 is also 1591 persons.

Substitute 1483 for *a* and 2001 for *b* in equation (1).

Therefore, average rate of change of population between 2002 and 2004 is

(c)

To determine

**To evaluate:** The time period for which population was increasing.

Expert Solution

For the time period 1997 to 2001 population was increasing

The given table is,

Year | Population |

1997 | 624 |

1998 | 856 |

1999 | 1336 |

2000 | 1578 |

2001 | 1591 |

2002 | 1483 |

2003 | 994 |

2004 | 826 |

2005 | 801 |

2006 | 745 |

It is clear from the table that from the year 1997 to 2001 the population of the coastal community is increasing continuously.

(d)

To determine

**To evaluate:** The time period for which population was decreasing.

Expert Solution

For the time period 2001 to 2006 population was decreasing

The given table is,

Year | Population |

1997 | 624 |

1998 | 856 |

1999 | 1336 |

2000 | 1578 |

2001 | 1591 |

2002 | 1483 |

2003 | 994 |

2004 | 826 |

2005 | 801 |

2006 | 745 |

It is clear from the table from the year 2001 to year 2006 the population of the coastal community is decreasing continuously.