the percentage of alcohol in a person's bloodstream t hr after drinking 8 fluid oz of whiskey is given by A(t)=0.23te^(-0.4t) (0<=t<=12) a) What is the percentage of alcohol in a person's bloodstream after 1/2 hr? And after 4 hr? b) How fast is the percentage of alcohol in a person's bloodstream changing after 1/2 hr? And after 4 hr?

Dawson Downs

Dawson Downs

Answered question

2022-07-17

the percentage of alcohol in a person's bloodstream t hr after drinking 8 fluid oz of whiskey is given by A ( t ) = 0.23 t e 0.4 t       ( 0 t 12 )
a) What is the percentage of alcohol in a person's bloodstream after 1 2 hr? And After 4 hr?
b) How fast is the percentage of alcohol in a person's bloodstream changing after 1 2 hr? And After 4 hr?

Answer & Explanation

Bradley Sherman

Bradley Sherman

Beginner2022-07-18Added 17 answers

Solution: percentage of alcohol in a person's bloodstream after "t" hr
A ( t ) = 0.23 t e 0.4 t ( 0 t 12 )
a) i) percentage of alcohol after 1 2 hr
A ( 1 2 ) = 0.23 ( 1 2 ) e 0.4 ( 1 2 ) = 0 23 2 e 0.2 A ( 1 2 ) = 0.094
ii) After 4 hours
A ( 4 ) = 0.23 ( 4 ) e 0.4 ( 4 ) = 0.92 e 1.6 A ( 4 ) = 0.186
b) Rate of change of percentage of alcohol is given by
A ( t ) = 0.23 [ e 0.4 t d d t ( t ) + t d d t ( e 0.4 t ) ] = 0.23 [ e 0.4 t + r e 0.4 t ( 0.4 ) ] A ( t ) = 0.23 e 0.4 t [ 1 0.4 t ]
i) Rate of change of percentage after 1 2 hr
A ( 1 2 ) = 0.23 e 0.4 ( 1 2 ) [ 1 0.4 ( 1 2 ) ] = 0.23 e 0.2 [ 1 0.2 ] = ( 0.23 ) ( 0.8 ) e 0.2 A ( 1 2 ) = 0.151
ii) After 4 hours
A ( 4 ) = 0.23 e 0.4 ( 4 ) [ 1 0.4 ( 4 ) ] = 0.23 e 1.6 [ 1 1.6 ] A ( 4 ) = 0.028

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