Explanation Given information: According to the US Department of Energy, the US industrial sector consumed about 721trillion BTUs of wind power in 2009. 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 721trillion BTUs of wind power in 2009. It means at 2009, t = 0 and E 0 = 721 trillion BTUs. Calculation: Steps Description E = E 0 a t ⇒ E = E 0 ( 1 + r ) t E = 721 ( 1 + − 4 % ) 1 = 721 ( 1 + − 4 100 ) 1 = 721 ( 1 − 0 To determine (b) To graph: The points showing the annual US consumption of wind power, in trillion BTUs, for the years 2009 to 2014. To determine (c) To find: The year when the largest yearly increase, in trillion BTUs, in the US consumption of wind power occurs and the increase.

Applied Calculus, 6e WileyPLUS + Loose-leaf

6th Edition

ISBN: 9781119408901

Author: Deborah Hughes-Hallett, Andrew M. Gleason, Patti Frazer Lock, Daniel E. Flath

Publisher: Wiley (WileyPLUS Products)

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Question

Chapter 1.5, Problem 44P

To determine

(a)

To find:

Amount of wind power (in trillion BTUs) US consumed in 2010 and in 2011.

To determine

(b)

To graph:

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

To determine

(c)

To find:

The year when the largest yearly increase, in trillion BTUs, in the US consumption of wind power occurs and the increase.

Expert Solution & Answer

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Chapter 1.5, Problem 43P

Chapter 1.5, Problem 45P

Chapter 1 Solutions

Applied Calculus, 6e WileyPLUS + Loose-leaf

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

Solution Summary: The author explains that the US industrial sector consumed about 721trillion BTUs of wind power in 2009. Exponential decay is often described in terms of percent decay rates.

Concept explainers

Videos

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

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

(c) To find: The year when the largest yearly increase, in trillion BTUs, in the US consumption of wind power occurs and the increase.

Want to see the full answer?

Chapter 1 Solutions

(a)

To find:

Amount of wind power (in trillion BTUs) US consumed in 2010 and in 2011.

(b)

To graph:

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

(c)

To find:

The year when the largest yearly increase, in trillion BTUs, in the US consumption of wind power occurs and the increase.