Chapter 6.3, Problem 44E

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10th Edition

Ron Larson

ISBN: 9781305860919

Textbook Problem

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**Electricity** The table shows the residential prices of electricity (in cents per kilowatt-hour) for the years 2006 through 2014. *(Source: U.S. Energy Information Administration)*

Year |
2006 | 2007 | 2008 | 2009 | 2010 | |

Price |
10.40 | 10.65 | 11.26 | 11.51 | 11.54 | |

Year |
2011 | 2012 | 2013 | 2014 | ||

Price |
11.72 | 11.88 | 12.12 | 12.54 |

Spreadsheet at LarsonAppliedCalculus.com

(a) Use Simpson’s Rule to estimate the average residential price of electricity over the time period.

(b) A model for the data is

*E* is the residential price of electricity (in cents per kilowatt-hour) and t is the year, with *t* = 6 corresponding to 2006. Use integration to find the average residential price of electricity over the time period.

(c) Compare the results of parts (a) and (b).

**(a)**

To determine

**To calculate:** The average Residential price of electricity over the time period using Simpson’s Rule for the table that shows the median ages of the U.S. resident population for the years 2006 through 2014.

Year | 2006 | 2007 | 2008 | 2009 | 2010 | 2011 | 2012 | 2013 | 2014 |

Median Age | 10.40 | 10.65 | 11.26 | 11.51 | 11.54 | 11.72 | 11.88 | 12..12 | 12.54 |

Explanation

**Given Information:**

The table shows the residential prices of electricity (in cents per Kilowatt-hour) for the years 2006 through 2014.

Year | 2006 | 2007 | 2008 | 2009 | 2010 | 2011 | 2012 | 2013 | 2014 |

Median Age | 10.40 | 10.65 | 11.26 | 11.51 | 11.54 | 11.72 | 11.88 | 12..12 | 12.54 |

**Formula used:**

Simpson’s Rule:

If *f* is continuous on *n* is an even integer, then

The average median can be find as,

**Calculation:**

Since, the given table shows the population from 2005 to 2013.

So, here

Now, use the table and substitute

**(b)**

To determine

**To calculate:** The average residential prices of electricity (in cents per Kilowatt-hour) over the time period for the model of data

**(c)**

To determine

The comparison between the results obtained from the average residential price of electricity by using table of data and the average residential price of electricity over the time period using model of the data.

Sect-6.1 P-1CPSect-6.1 P-2CPSect-6.1 P-3CPSect-6.1 P-4CPSect-6.1 P-5CPSect-6.1 P-6CPSect-6.1 P-7CPSect-6.1 P-1SWUSect-6.1 P-2SWUSect-6.1 P-3SWU

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