Explanation Given: The drug concentration curve is C = f ( t ) = 20 t e − 0.04 t Formula Used: Product rule of derivative is as follows: ( f . g ) ′ = f ′ . g + f . g ′ Calculation: Given that a drug concentration curve is C = f ( t ) = 20 t e − 0.04 t Graph of drug concentration against time is plotted as follows: We need to calculate f ′ ( t ) f ′ ( t ) = d d t ( 20 t e − 0.04 t ) f ′ ( t ) = 20 d d t ( t e − 0.04 t ) Using product rule of derivative, we have f ′ ( t ) = 20 [ d d t ( t ) × ( e − 0.04 t ) + ( t ) × d d t ( e − 0.04 t ) ] f ′ ( t ) = 20 [ ( 1 ) ( e − 0.04 t ) + ( t ) ( − 0.04 e − 0.04 t ) ] f ′ ( t ) = 20 [ e − 0.04 t − 0.04 t e − 0.04 t ] f ′ ( t ) = 20 e − 0.04 t [ 1 − 0.04 t ] f ′ ( 15 ) is calculated by substituting t = 15 in f ′ ( t ) = 20 e − 0.04 t [ 1 − 0.04 t ] f ′ ( 15 ) = 20 e − 0 To determine (b) Given that a drug concentration curve is C = f ( t ) = 20 t e − 0.04 t To find f ( 30 ) and f ′ ( 30 )

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 3.4, Problem 41P

To determine

(a)

Graph the concentration C against time t, given that a drug concentration curve is

C=f(t)=20te−0.04t

Also, find f′(15) and f′(45) is positive or negative.

To determine

(b)

Given that a drug concentration curve is

C=f(t)=20te−0.04t

To find f(30) and f′(30)

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Chapter 3.4, Problem 40P

Chapter 3.4, Problem 42P

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(a) Graph the concentration C against time t , given that a drug concentration curve is C = f ( t ) = 20 t e − 0.04 t Also, find f ′ ( 15 ) and f ′ ( 45 ) is positive or negative.

Solution Summary: The author explains how to calculate the drug concentration against time using the product rule of derivative.

Videos

(a)

Graph the concentration C against time t, given that a drug concentration curve is

C=f(t)=20te−0.04t

Also, find f′(15) and f′(45) is positive or negative.

(b)

Given that a drug concentration curve is

C=f(t)=20te−0.04t

To find f(30) and f′(30)

Want to see the full answer?

Chapter 3 Solutions

(a) Graph the concentration C against time t , given that a drug concentration curve is C = f ( t ) = 20 t e − 0.04 t Also, find f ′ ( 15 ) and f ′ ( 45 ) is positive or negative.

Solution Summary: The author explains how to calculate the drug concentration against time using the product rule of derivative.

Videos

(a) Graph the concentration C against time t, given that a drug concentration curve is C=f(t)=20te−0.04t Also, find f′(15) and f′(45) is positive or negative.

(b) Given that a drug concentration curve is C=f(t)=20te−0.04t To find f(30) and f′(30)

Want to see the full answer?

Chapter 3 Solutions

(a)

Graph the concentration C against time t, given that a drug concentration curve is

C=f(t)=20te−0.04t

Also, find f′(15) and f′(45) is positive or negative.

(b)

Given that a drug concentration curve is

C=f(t)=20te−0.04t

To find f(30) and f′(30)