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.

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Chapter 1.5, Problem 43P

Chapter 1.5, Problem 45P

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Chapter 1 Solutions

Applied Calculus, 6e WileyPLUS + Loose-leaf

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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.

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(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.

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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.