   Chapter 6.3, Problem 44E ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

#### Solutions

Chapter
Section ### Calculus: An Applied Approach (Min...

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 = 516.23254 e − t +   0.0182 t 3 −   0.595 t 2 +   6.58 t   −   12.9 for 6 ≤ t ≤ 14 , where 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 10.4 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 10.4 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 [a,b] and n is an even integer, then

abf(x)dx=(ba3n)[f(x0)+4f(x1)+2f(x2)+4f(x3)++4f(xn1)+f(xn)]

The average median can be find as,

Average price of Electricity=1baabf(x)dx

Calculation:

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

So, here a=6 and b=14

Now, use the table and substitute a=6,b=14 and n=8 in the Simpson’s formula as,

abf(x)dx=1463×8[10.40+4(10.65)+2(11.26)+4(11.51)+2(11.54)+4(11.72)+2(11

(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 E=516.23254et+0.0182t30.595t2+6.58t12.9.

(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.

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