Explanation Given information: According to the US Department of Energy, the US industrial sector consumed about 2.65 quadrillion BTUs of hydroelectric power in 2009. Year 2009 2010 2011 2012 2013 2014 % growth 6.3 -4.9 22.4 -15.5 -3.0 -3.4 Concept involved: The function f ( x ) = 2 x , where the power is variable, is an exponential function. The number is called the base. Exponential functions of the form f ( x ) = k ⋅ a x , where a is a positive constant, are used to represent many phenomena in the natural and social sciences. The General Exponential Function: Exponential decay is often described in terms of percent decay rates. We say that W is an exponential function of t with base a if W = W 0 a t , where W 0 is the initial amount (when t = 0 ) and a is the factor by which W changes when t increases by 1. If a>1, we have exponential growth; if 0 < a < 1 , we have exponential decay. The factor a is given by a = 1 + r where r is the decimal representation of the percent rate of change; r may be positive (for growth) or negative (for decay). According to the US Department of Energy, the US consumed 2.65 quadrillion BTUs of hydroelectric power in 2009. It means at 2009, t = 0 and E 0 = 2.65 quadrillion BTUs Calculation: Steps Description E = E 0 a t ⇒ E = E 0 ( 1 + r ) t E = 2 To determine (b) To graph: The points showing the annual US consumption of hydroelectric power, in quadrillion BTUs of hydroelectric power, for the years 2009 to 2014. To determine (c) To find: The year when the largest yearly decrease, in quadrillion BTUs, in the US consumption of hydroelectric power occurs and the decrease.

6th Edition

ISBN: 9781119399353

Author: DA

Publisher: JOHN WILEY+SONS,INC.-CONSIGNMENT

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Question

Chapter 1.5, Problem 43P

To determine

(a)

To find:

Amount of hydroelectric power (in quadrillion BTUs) US consumed in 2010 and in 2011.

To determine

(b)

To graph:

The points showing the annual US consumption of hydroelectric power, in quadrillion BTUs of hydroelectric power, for the years 2009 to 2014.

To determine

(c)

To find:

The year when the largest yearly decrease, in quadrillion BTUs, in the US consumption of hydroelectric power occurs and the decrease.

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Chapter 1.5, Problem 42P

Chapter 1.5, Problem 44P

Chapter 1 Solutions

EBK APPLIED CALCULUS, ENHANCED ETEXT

Ch. 1.1 - Prob. 1P Ch. 1.1 - Prob. 2P Ch. 1.1 - Prob. 3P Ch. 1.1 - Prob. 4P Ch. 1.1 - Prob. 5P Ch. 1.1 - Prob. 6P Ch. 1.1 - Prob. 7P Ch. 1.1 - Prob. 8P Ch. 1.1 - Prob. 9P Ch. 1.1 - Prob. 10P

Ch. 1.1 - Prob. 11P Ch. 1.1 - Prob. 12P Ch. 1.1 - Prob. 13P Ch. 1.1 - Prob. 14P Ch. 1.1 - Prob. 15P Ch. 1.1 - Prob. 16P Ch. 1.1 - Prob. 17P Ch. 1.1 - Prob. 18P Ch. 1.1 - Prob. 19P Ch. 1.1 - Prob. 20P Ch. 1.1 - Prob. 21P Ch. 1.1 - Prob. 22P Ch. 1.1 - Prob. 23P Ch. 1.1 - Prob. 24P Ch. 1.1 - Prob. 25P Ch. 1.1 - Prob. 26P Ch. 1.1 - Prob. 27P Ch. 1.1 - Prob. 28P Ch. 1.1 - Prob. 29P Ch. 1.1 - Prob. 30P Ch. 1.1 - Prob. 31P Ch. 1.1 - Prob. 32P Ch. 1.1 - Prob. 33P Ch. 1.1 - Prob. 34P Ch. 1.1 - Prob. 35P Ch. 1.1 - Prob. 36P Ch. 1.1 - Prob. 37P Ch. 1.1 - Prob. 38P Ch. 1.1 - Prob. 39P Ch. 1.1 - Prob. 40P Ch. 1.2 - Prob. 1P Ch. 1.2 - Prob. 2P Ch. 1.2 - Prob. 3P Ch. 1.2 - Prob. 4P Ch. 1.2 - Prob. 5P Ch. 1.2 - Prob. 6P Ch. 1.2 - Prob. 7P Ch. 1.2 - Prob. 8P Ch. 1.2 - Prob. 9P Ch. 1.2 - Prob. 10P Ch. 1.2 - Prob. 11P Ch. 1.2 - Prob. 12P Ch. 1.2 - Prob. 13P Ch. 1.2 - Prob. 14P Ch. 1.2 - Prob. 15P Ch. 1.2 - Prob. 16P Ch. 1.2 - Prob. 17P Ch. 1.2 - Prob. 18P Ch. 1.2 - Prob. 19P Ch. 1.2 - Prob. 20P Ch. 1.2 - 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Prob. 102SYU Ch. 1 - Prob. 103SYU Ch. 1 - Prob. 104SYU Ch. 1 - Prob. 105SYU

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(a) To find: Amount of hydroelectric power (in quadrillion BTUs) US consumed in 2010 and in 2011.

Solution Summary: The author explains that the US industrial sector consumed about 2.65 quadrillion BTUs of hydroelectric power in 2009. Exponential decay is often described in terms of percent decay rates.

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(a) To find: Amount of hydroelectric power (in quadrillion BTUs) US consumed in 2010 and in 2011.

(b) To graph: The points showing the annual US consumption of hydroelectric power, in quadrillion BTUs of hydroelectric power, for the years 2009 to 2014.

(c) To find: The year when the largest yearly decrease, in quadrillion BTUs, in the US consumption of hydroelectric power occurs and the decrease.

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Chapter 1 Solutions

(a)

To find:

Amount of hydroelectric power (in quadrillion BTUs) US consumed in 2010 and in 2011.

(b)

To graph:

The points showing the annual US consumption of hydroelectric power, in quadrillion BTUs of hydroelectric power, for the years 2009 to 2014.

(c)

To find:

The year when the largest yearly decrease, in quadrillion BTUs, in the US consumption of hydroelectric power occurs and the decrease.