   Chapter 8.5, Problem 59E ### 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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# Consumer Trends Energy consumption in the United States is seasonal. The primary residential energy consumption Q (in trillion Btu) in the United States during 2014 can be modeled by Q = 916 + 727.8   cos ( 0.33 t + 0.751 ) , 0 ≤ t ≤ 12 Where t is the time (in months), with t = 1 corresponding to January. Find the average primary residential energy consumption during the first quarter ( 0 ≤ t ≤ 3 ) . the fourth quarter ( 9 ≤ t ≤ 12 ) . the entire year ( 0 ≤ t ≤ 12 ) .(Source: U.S. Energy Information Administration)

(a)

To determine

To calculate: The average primary residential energy consumption during first quarter 0t3, when primary residential energy consumption Q in trillion Btu in United State during 2014 is Q=916+727.8cos(0.33t+0.751) for 0t12.

Explanation

Given Information:

The primary residential energy consumption Q in trillion Btu in United State during 2014 is given as Q=916+727.8cos(0.33t+0.751) for 0t12.

Formula used:

Write the formula for average value of a provided function f(x) for [a,b].

Average value=1baabf(x)dx

Write the formula for definite integral of abcosnudu.

abcosnudu=[sinnun]ab

Write the formula for integral of abdu.

abdu=[u]ab

Calculation:

The average primary residential energy consumption during first quarter 0t3 can be calculated as:

QFirst Quater=13003[916+727

(b)

To determine

To calculate: The average primary residential energy consumption during fourth quarter 9t12, when primary residential energy consumption Q in trillion Btu in United State during 2014 is given as Q=916+727.8cos(0.33t+0.751) for 0t12.

(c)

To determine

To calculate: The average primary residential energy consumption during whole year 0t12, when primary residential energy consumption Q in trillion Btu in United State during 2014 is given as Q=916+727.8cos(0.33t+0.751) for 0t12.

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