Explanation Given: ACME Widgets sold widgets at a continuous rate of R = R o e 0.125 t , where t is time in years since January 1, 2005. Also, they were selling widgets at a rate of 1000 per year on January 1, 2005. Calculation: Consider the continuous rate for sold widget per year since 2005. R = R o e 0.125 t Consider for R o = 1000 Thus, we have rate as R = 1000 e 0.125 t Consider t = 0 for 2005 and t = 10 for 2015. Now widgets sold between year 2005 to 2015 is calculated as follows: S = ∫ 0 10 1000 e 0.125 t d t = 1000 ∫ 0 10 e 0.125 t d t Let u = 0.125 t , d u d t = 0.125 and d t = d u 0.125 When t = 0 , u = 0 When t = 10 , u = 0.125 × 10 = 1.25 ∫ 0 10 1000 e 0.125 t d t = 1000 ∫ 0 1.25 e u 0.125 d u = 1000 0.125 ∫ 0 1.25 e u d u = 1000 0.125 [ e u ] 0 1.25 = 1000 0.125 [ e 1.25 − e 0 ] = 8000 [ 3.490 − 1 ] = 8000 × 2 To determine (b) To find the number of years after 2005 half number of widgets are sold. To determine (c) ACME advised that half the widgets it had sold in the previous ten years were till in use. To find how long must a widget last in order to justify this claim

6th Edition

ISBN: 9781119399353

Author: DA

Publisher: JOHN WILEY+SONS,INC.-CONSIGNMENT

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Chapter 6.3, Problem 33P

To determine

(a)

To find the number of widgets sold between 2005 and 2015.

To determine

(b)

To find the number of years after 2005 half number of widgets are sold.

To determine

(c)

ACME advised that half the widgets it had sold in the previous ten years were till in use. To find how long must a widget last in order to justify this claim

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Chapter 6.3, Problem 32P

Chapter 6.3, Problem 34P

Chapter 6 Solutions

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(a) To find the number of widgets sold between 2005 and 2015.

Solution Summary: The author explains how ACME Widgets sold widgets at a continuous rate of R=R_oe0.125t, where t is time in years since January

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(a) To find the number of widgets sold between 2005 and 2015.

(b) To find the number of years after 2005 half number of widgets are sold.

(c) ACME advised that half the widgets it had sold in the previous ten years were till in use. To find how long must a widget last in order to justify this claim

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Chapter 6 Solutions

(a)

To find the number of widgets sold between 2005 and 2015.

(b)

To find the number of years after 2005 half number of widgets are sold.

(c)

ACME advised that half the widgets it had sold in the previous ten years were till in use. To find how long must a widget last in order to justify this claim