   Chapter 13, Problem 14T ### 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

# With data from the U.S. Department of Energy, the number of billions of barrels of U.S. crude oil produced per year from 2010 and projected to 2030 can be modeled by the function f ( t )   = − 0.0001 t 2 +   0.037 t   +   1.94 where t is the number of years past 2010.(a) Find the total number of barrels of oil produced from 2010 to 2020.(b) Find the average number of barrels produced per year from 2010 to 2018.

(a)

To determine

To calculate: The total number of barrels of oil produced from the year 2010 to 2020 if the number of billions of barrels of oil produced per year from 2010 and projected to 2030 is provided by the function f(t)=0.001t2+0.037t+1.94, where t is the number of years past 2010.

Explanation

Given Information:

The number of billions of barrels of oil produced per year from 2010 and projected to 2030 is provided by the function f(t)=0.001t2+0.037t+1.94, where t is the number of years past 2010.

Formula used:

The power rule of integral is xndx=xn+1n+1+C, where n1.

Calculation:

Consider the function,

f(t)=0.001t2+0.037t+1.94

From 2010 to 2020, the number of years t is,

t=20202010=10

The total number of barrels of oil produced from the year 2010 to 2020 is,

010f(t)dt=010(0

(b)

To determine

To calculate: The average number of barrels of oil produced per year from 2010 to 2018 if the number of billions of barrels of oil produced per year from 2010 and projected to 2030 is provided by the function f(t)=0.001t2+0.037t+1.94, where t is the number of years past 2010.

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