   Chapter 13.6, Problem 38E ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# Natural gas The percent of natural gas in the United States extracted from shale rock from 2012 and projected to 2040 is given by the function y =   − 0.843   +   13.8  ln  x , where x is the is the number of years after 2010 (Source: Energy Information Administration). What does this model project the average percent to be for the years 2015 through 2030?

To determine

To calculate: The average percent to be for the years 2015 through 2030 if the percent of natural gas in the United States extracted from shale rock from 2012 and projected to 2040 is given by the function y=0.843+13.8lnx. Here, x represent the no. of years past 2010.

Explanation

Given Information:

The percent of natural gas in the United States extracted from shale rock from 2012 and projected to 2040 is given by the function y=0.843+13.8lnx. Here, x represent the number of years after 2010.

Formula used:

The power rule of integration is;

The integration of function f(x)=xn is given by;

xndx=xn+1n+1+c n1

Here c is any arbitrary constant.

The integration by parts formula is;

uvdx=uvdxdudx(vdx)dx

The sum rule is;

f(x)±g(x)dx=f(x)dx±g(x)dx

Calculation:

Consider the percent of natural gas in the United States extracted from shale rock from 2012 and projected to 2040 is given by the function,

y=0.843+13.8lnx

Here, x represent the number of years after 2010.

Consider the years as,

20152010=520302010=20

The average percent to be for the years 2015 through 2030 will be;

520ydx520dx=520ydx15

Integrate the function as;

y(x)dx=0

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