Explanation Given: The quantity of a drug present in the body t hours after an injection of drug is given as Q = f ( t ) = 100 t e − 0.5 t . Formula Used: Product rule of derivative is as follows: ( f . g ) ′ = f ′ . g + f . g ′ Calculation: Given that the quantity of a drug present in the body t hours after an injection of drug is given as Q = f ( t ) = 100 t e − 0.5 t . We need to calculate f ′ ( t ) . f ′ ( t ) = d d t ( 100 t e − 0.5 t ) f ′ ( t ) = 100 d d t ( t e − 0.5 t ) Using product rule of derivative, we have f ′ ( t ) = 100 [ d d t ( t ) × ( e − 0.5 t ) + ( t ) × d d t ( e − 0.5 t ) ] f ′ ( t ) = 100 [ ( 1 ) × ( e − 0.5 t ) + ( t ) × ( − 0.5 e − 0.5 t ) ] f ′ ( t ) = 100 [ e − 0.5 t − 0.5 t e − 0.5 t ] f ′ ( t ) = 100 e − 0.5 t [ 1 − 0.5 t ] . f ( 1 ) is calculated by substituting t = 1 in f ( t ) = 100 t e − 0.5 t . f ( 1 ) = 100 ( 1 ) e − 0.5 × 1 f ( 1 ) = 100 e − 0.5 f ( 1 ) = 60.65 m g After 1 h o u r , quantity of a drug present in the body is 60.65 m g . f ′ ( 1 ) is calculated by substituting t = 1 in f ′ ( t ) = 100 e − 0

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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Chapter 3.4, Problem 40P

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To find f(1),f′(1),f(5) and f′(5), given that the quantity of a drug present in the body t hours after an injection of drug is given as

Q=f(t)=100te−0.5t.

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Chapter 3.4, Problem 39P

Chapter 3.4, Problem 41P

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To find f ( 1 ) , f ′ ( 1 ) , f ( 5 ) and f ′ ( 5 ) , given that the quantity of a drug present in the body t hours after an injection of drug is given as Q = f ( t ) = 100 t e − 0.5 t .

Solution Summary: The author calculates the quantity of a drug present in the body t hours after an injection of drug.

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To find f(1),f′(1),f(5) and f′(5), given that the quantity of a drug present in the body t hours after an injection of drug is given as

Q=f(t)=100te−0.5t.

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Chapter 3 Solutions

To find f ( 1 ) , f ′ ( 1 ) , f ( 5 ) and f ′ ( 5 ) , given that the quantity of a drug present in the body t hours after an injection of drug is given as Q = f ( t ) = 100 t e − 0.5 t .

Solution Summary: The author calculates the quantity of a drug present in the body t hours after an injection of drug.

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To find f(1),f′(1),f(5) and f′(5), given that the quantity of a drug present in the body t hours after an injection of drug is given as Q=f(t)=100te−0.5t.

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Chapter 3 Solutions

To find f(1),f′(1),f(5) and f′(5), given that the quantity of a drug present in the body t hours after an injection of drug is given as

Q=f(t)=100te−0.5t.